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The harmonic two-colour excitation of a two-level molecule, where the frequencies of the two continuous wave lasers are multiples of a certain frequency, is studied in the rotating wave approximation (RWA) and by using exact methods. Included are the effects of a non-zero different *d* between the permanent dipole moments of the two states involved in the transition. For two independent frequencies, the two-colour RWA yields analytical results only when one two-colour resonance dominates the transition, while for the harmonic analogue, analytic solutions, exhibiting the effects of both laser and molecular parameters, are available for problems involving competing two-colour resonances. Analytical solutions for both the time-dependent populations of the excited state, and for the associated resonance profiles, are derived, applied to a model two-level molecule, and tested by comparison with exact results obtained using Floquet techniques. The results are used to discuss the phase control of molecular excitation through the interplay of competing resonance involving the effects of *d* ≠ 0; the competition vanishes if *d* = 0. Both fixed molecule-laser configurations, and the effects of orientational averaging, are considered.

The effects of permanent dipole moments and those due to the randomness of molecular orientation in the phase control of molecular excitation are discussed for the simultaneous one- and three-photon excitation of a two-level model molecule. In this transition scheme both transitions can occur with or without the presence of permanent dipoles and the results are contrasted to those corresponding to the one- and two-photon excitation of a two-level molecule, which requires the presence of permanent dipoles. The dependence of the temporal evolution of the excited state and the associated resonance profiles on the relative phase of the lasers is used to monitor the control of the excitation process. Analytical perturbation theory, the rotating-wave approximation, and exact Floquet results for those observables are used for this purpose. Both fixed molecule-laser configurations and situations where the absorbing molecules assume random orientations with respect to the laser beams are considered.

The absolute laser phase dependence of the time-dependent populations of the molecular states, including the steady-state (long time) populations of the states, associated with the interaction of a molecule with a pulsed laser is investigated using illustrative two-level examples. One-photon transitions, including the effects of permanent dipoles, are discussed as a function of the pulse duration, intensity, and (absolute) laser phase, for selected laser frequencies. The effects of laser phase can be large, depending on the values of the pulse duration for a given frequency and intensity. The effects of permanent dipoles, relative to no permanent dipoles, are significant for large laser field strengths ε0. When the laser-molecule coupling parameter b=μ12ε0/E21⩾0.2, where μ12 and E21 are the transition dipole and energy difference between the ground and excited states, respectively, the dynamics of the pulse-molecule interaction are (strongly) phase dependent, independent of pulse duration, whereas the corresponding steady-state populations of the molecular states may or may not be phase-dependent depending on the pulse duration. Analytical rotating wave approximations for pulsed laser-molecule interactions are useful for interpreting the dynamics and the steady-state results as a function of field strength and pulse duration, including the effects of permanent dipole moments. The results reported in this paper are based on molecular parameters associated with an S0→S1 electronic transition in a dipolar molecule. However, they are presented in reduced form and therefore can be scaled to other regions of the electromagnetic spectrum. Short, intense pulses at or beyond the limits of current laser technology will often be required for the types of absolute laser phase effects of this paper to be appreciable for electronic excitations. The discussion, in the UV-VIS, also suffers from the use of a two-level model and from the requirement of field intensities that can be beyond the Keldysh limit. For other spectral regions, these absolute laser phase effects will be much more readily applicable.

Adiabatic potential energy surfaces of the three lowest lying singlet states, X̃ 1A‘ 2 1A‘, and 11A‘ ‘, of N2O have been computed as a function of the *R*N2-O bond distance and the Jacobi angle. The calculations are performed using the complete-active-space self-consistent field (CASSCF) and the multireference configuration interaction (MRCI) electronic structure methods. It is shown that there is a wide avoided crossing between the ground, X̃ 1A‘, and lowest excited, 2 1A‘, electronic state. This avoided crossing is thought to give rise to a seam of conical intersection at other N−N separations. Both excited state surfaces display important conical intersections at linear geometries. The transition dipole moment surfaces for the two excitation processes (2 1A‘ ← X̃ 1A‘ and 1 1A‘ ‘ ← X̃ 1A‘) are also presented. These calculations provide the basic data needed to compute the dynamics of the N2O + *h*ν → N2 + O(1D) photodissociation process for photon frequencies in the range 5.2 eV (240 nm) to 7.3 eV (170 nm).

A rotating-wave approximation (RWA) is developed to describe the evolution of a two-level system, which has permanent dipole moments, interacting with a pulsed laser. Comparisons with exact calculations for one- and two-photon excitations involving the two lowest vibrational states of the ground electronic state of HeH+ are given to illustrate the validity of the RWA formula.

A general and computationally efficient method for averaging both the time-dependent and the steady-state atomic or molecular state populations over the phases, δ1 and δ2, of two continuous-wave laser fields involved in an excitation process is developed based on the Floquet formalism. Explicit calculations are presented for the coherent one- and three-photon electronic excitation of a two-level model molecule in order to illustrate the importance of phase averaging in situations where the relative phase difference between the two fields is fixed. While the explicit results involve electronic excitation, they are presented in reduced form so that they can be scaled to other regions of the electromagnetic spectrum and to other field strengths. The results have important implications in situations where the relative phase difference between two intense continuous-wave laser fields is used to control the excitation process.

The photodissociation dynamics of HF and DF, following A 1Π←X 1Σ+ electronic excitation, are examined using time-dependent wave packet techniques. The calculations are based on new multireference configuration interaction calculations of the potential energy curves and complete active space self-consistent field calculations of the off-diagonal spin–orbit coupling matrix elements. The calculated branching fraction for the formation of excited state fluorine, F*(2P1/2),following excitation from the ground vibrational state(v=0) of HF, agrees well with the value of 0.41±0.08measured experimentally at 121.6 nm by Zhang et al. [J. Chem. Phys. **104**, 7027 (1996)]. Predictions are made for the excited spin–orbit state branching fraction for both HF and DF over a wide range of photonexcitation energies. The results for HF and DF are discussed in context with the corresponding results for the photodissociation of HCl and DCl.

The vibrationally mediated photodissociation dynamics of HF and DF, following A 1Π←X 1Σ+electronic excitation, are examined using time-dependent wave packet techniques. Predictions of the branching fraction for the formation of excited state fluorine, F(2P1/2), are made for a wide range of excitation energies and for the initial vibrational statesv=1, 2, and 3. The preceding article (Ref. 33) discusses the underlying theory and presents results for photodissociation from the ground vibrational state(v=0). The calculated branching fraction for HF photodissociation from the v=3vibrational state agrees well with the value of 0.42±0.03measured experimentally at 193.3 nm by Zhang et al. [J. Chem. Phys. **104**, 7027 (1996)]. The results are discussed in context with the corresponding results for HCl and DCl.

A procedure is presented for the calculation of the double vibrational collision-induced absorption CO_{2} (ν_{3} = 1) + N_{2} (ν_{1} = 1) ← CO_{2} (ν_{3} = 0) + N_{2} (ν_{1} = 0) on the basis of quantum lineshapes computed using an isotropic potential and dipole-induced dipole functions. The linestrengths and energies of the vibration–rotation transitions are treated explicitly for N_{2}, utilizing the HITRAN database for CO_{2}. The theoretical absorption profile is compared to recent experimental results. By narrowing the width of the individual lines contributing to the overall absorption profile relative to their values determined for N_{2}–N_{2} collision-induced absorption, excellent agreement between theory and experiment is obtained.

Experimental and theoretical methods have been applied to investigate the effect of internal parent excitation on the ultraviolet photodissociationdynamics of HCl (X 1Σ+) molecules. Jet-cooled H35Cl molecules within a time-of-flightmass spectrometer were prepared by infra-red absorption in the following quantum states: v=1, J=0 and J=5; v=2, J=0 and J=11; v=3, J=0and J=7. The excited molecules were then photodissociated at λ∼235 nm and the Cl(2Pj)photofragments detected using (2+1) resonance enhanced multiphoton ionization. The results are presented as the fraction of total chlorine yield formed in the spin–orbit excited state,Cl(2P1/2). The experimental measurements are compared with the theoretical predictions from a time-dependent, quantum dynamical treatment of the photodissociationdynamics of HCl (v=1−3, J=0). These calculations involved wavepacket propagation using the *ab initio*potential energy curves and coupling elements previously reported by Alexander, Pouilly, and Duhoo [J. Chem. Phys. **99**, 1752 (1993)]. The experimental results and theoretical predictions share a common qualitative trend, although quantitative agreement occurs only for HCl (v=2).

When O_{2} is perturbed by collisions with other molecules, the weak spin-forbidden magnetic dipole transition*a*^{1}Δ_{g}←*X*^{3}Σ_{g}^{−} shows a broad continuum absorption underlying the sharp lines. This collision-induced enhancement absorption plays a role in the Earth’s atmosphere and much experimental work has been carried out to measure the binary absorption coefficient with different perturber gases. Recent work on the *v*′=0←*v*=0 band in O_{2}–CO_{2} mixtures yielded a value for the coefficient that was approximately three times that of earlier measurements on O_{2}–N_{2} mixtures. In the present note, we calculate the absorption theoretically assuming that the long-range quadrupole-induced dipole mechanism is dominant. Using experimental polarizability matrix elements of CO_{2} and *ab initio* results in the literature for the quadrupolar transition matrix element for O_{2}, we find good agreement for O_{2}–CO_{2} mixtures without any adjustable parameters. The agreement for O_{2}–N_{2} is less good, and because of the much smaller polarizability of N_{2}than of CO_{2}, we suggest that one has to include a short-range component in addition to the long-range one treated here. We also calculate the binary absorption coefficient for O_{2}–H_{2}O, for which no experimental data are available, and we synthesize the corresponding spectrum for use in atmospheric modeling.

An experimental value for the quadrupole transition moment of the ν2 fundamental band of CH4has been determined by fitting the collision-induced enhancement spectrum of CH4 with Ar as the perturber. The observed quadrupole-induced absorption increases linearly with the Ar density, ρAr, and is comparable to the allowed dipole intensity due to Coriolis interaction with the ν4 band at approximately 125 amagats. Ignoring vibration-rotation interaction and Coriolis interaction,, we equate the measured slope of the integrated intensity versus ρAr to the theoretical expression for the quadrupole-induced absorption, and obtain the value |⟨0|Q|ν2⟩|=0.445 ea20 for the quadrupole transition matrix element. A theoretical value ⟨0|Q|ν2⟩=0.478 ea20 has been determined by large-scale *ab initio* calculations and, considering both the theoretical approximations and experimental uncertainties, we regard the agreement as good, thus confirming our interpretation of the enhancement as due to the quadrupole collision-induced mechanism.

The photodissociation of jet-cooled IBr molecules has been investigated at numerous excitation wavelengths in the range 440–685 nm using a state-of-art ion imaging spectrometer operating under optimal conditions for velocity mapping. Image analysis provides precise threshold energies for the ground, I(2P3/2)+Br(2P3/2), and first excited [I(2P3/2)+Br(2P1/2)]dissociation asymptotes, the electronic branching into these two active product channels, and the recoil anisotropy of each set of products, as a function of excitation wavelength. Such experimental data have allowed mapping of the partial cross-sections for parallel (i.e., ΔΩ=0) and perpendicular (i.e., ΔΩ=±1)absorptions and thus deconvolution of the separately measured (room temperature) parent absorptionspectrum into contributions associated with excitation to the A 3Π(1), B 3Π(0+) and 1Π(1)excited states of IBr. Such analyses of the continuous absorptionspectrum of IBr, taken together with previous spectroscopic data for the bound levels supported by the *A* and *B* state potentials, has allowed determination of the potential energy curves for, and (*R* independent) transition moments to, each of these excited states. Further wave packet calculations, which reproduce, quantitatively, the experimentally measured wavelength dependent product channel branching ratios and product recoil anisotropies, serve to confirm the accuracy of the excited state potential energy functions so derived and define the value (120 cm−1) of the strength of the coupling between the bound (B) and dissociative(Y) diabatic states of 0+ symmetry.

DOBr photoabsorption cross-sections and product rotational state distributions of the OD fragment resulting from excitation to the two lowest-lying excited singlet electronic states, 1^{1}A″ and 2^{1}A′, are computed using time-dependent wavepacket dynamics. The dynamical calculations are based on two-dimensional *ab initio* potential energy and transition dipole moment surfaces, in which the OD bond length is held fixed. The computed absorption band for DOBr is very similar to that of HOBr for excitation from the ground vibrational state. For vibrationally mediated photofragmentation spectra in which the initial state is a vibrationally excited state, the absorption line shape for DOBr differs markedly from the corresponding HOBr absorption. For all initial vibrational states, the resulting OD fragments are produced more rotationally “hot” than their OH counterparts. The resulting OD and OH rotational distributions agree qualitatively with experimental measurements at 266 nm, where the excitation is dominated by the parallel 2 ^{1}A′←^{1}A′ transition. Predictions are also made for the rotational distributions at 355 nm, where the perpendicular transition 1^{1}A″←^{1}A′ is dominant and no experimental product state distributions are as yet available.

Total absorption cross-sections and product rotational quantum state distributions are computed from first principles for the first two ultraviolet absorption bands of the HOBr molecule corresponding to excitation to the 1^{1}A″ and 2^{1}A′ states. The dynamical calculations are based on*ab initio* potential energy surfaces and transition dipole moment surfaces. The theory of triatomic photodissociation is presented in detail, in a manner which is clearer than previously available, and an important correction is made to the theoretical formulae. The theory takes proper account of angular momentum coupling and of the parity of all of the constituent wavefunctions. It is applicable to any initial (or final) angular momentum. The computed absorption bands agree reasonably well with available experimental results but highlight shortcomings of the electronic structure calculations on which these dynamical calculations are based. Predictions are made for the effect of excitation of initial vibrational states on the absorption line shapes.

The double vibrational collision-induced absorptions CO_{2} (ν_{3} = 1) + *X*_{2} (ν_{1} = 1) ← CO_{2} (ν_{3} = 0) + *X*_{2} (ν_{1} = 0), for *X*_{2} = H_{2}, N_{2}, and O_{2} are studied on the basis of quantum lineshapes computed using isotropic potentials and dipole-induced dipole functions. The linestrengths and energies of the vibration–rotation transitions are treated explicitly for *X*_{2} and utilizing the HITRAN database for CO_{2}. From the frequency-dependent absorption profiles, the integrated absorption intensities are determined to be 7.2 ± 1.2, 1.2 ± 0.1, and 1.1 ± 0.2 (10^{−4} cm^{−2} amagat^{−2}) for the H_{2}, N_{2}, and O_{2} collision partners, respectively. The integrated intensities for H_{2} and N_{2} agree well with previously measured and calculated results, while the value for O_{2}, which represents the first theoretical determination for this absorption, is approximately four times greater than the only experimental measurement (0.29 × 10^{−4} cm^{−2} amagat^{−2}).

in Time-dependent Quantum Dynamics, edited by S.C. Althorpe, P. Soldan, and G.G. Balint-Kurti (CCP6, Daresbury, 2001), 83-88.

Publication year: 2001

The pump-probe excitation of a two-level dipolar (d≠0) molecule, where the pump frequency is tuned to the energy level separation while the probe frequency is extremely small, is examined theoretically as an example of absolute phase control of excitation processes. The state populations depend on the probe field’s absolute carrier phase but are independent of the pump field’s absolute carrier phase. Interestingly, the absolute phase effects occur for pulse durations much longer and field intensities much weaker than those required to see such effects in single pulse excitation.

The integrated intensities of the collision-induced enhancement spectra of the ν2 band of CH4perturbed by rare gases and linear molecules (N2, H2, and CO2) are calculated theoretically using the quadrupoletransition moment obtained from an analysis of CH4–Ar spectra. In addition to the isotropic quadrupole mechanism responsible for the enhancement in CH4-rare gases, there is additional absorption arising from the anisotropicquadrupole mechanism in the case of molecular perturbers. This latter effect involves the matrix element of the anisotropicpolarizability for the ν2transition in CH4 that is available from the analysis of the depolarized Raman intensity measurements. Overall, the theoretical values for the slope of the enhancement spectra with respect to the perturber density are in reasonably good agreement with the experimental results, thus confirming that the collision-induced absorption arises primarily through the quadrupolar induction mechanism.

The excitation of a two-level dipolar (d≠0) molecule with two Gaussian pulsed lasers is examined theoretically for the case where one laser’s frequency is tuned close to the energy level separation (pump laser) while the second laser’s frequency is extremely small (probe laser). The final excited state populations are shown to depend on the probe laser’s absolute carrier phase while remaining independent of the pump laser’s absolute carrier phase. They do not depend on the relative phase difference between the two laser fields as in many other pump-probe scenarios. The absolute carrier-phase effect is negligible for nondipolar (d=0) molecules. The probe laser absolute carrier-phase effect arises through the coherent excitation of multiple optical paths from the initial to the final state containing a common number of pump photons (Npump=1) and a varying number of probe photons. Excited state populations, after the interaction of the pulses with the molecule is complete, are examined as a function of the probe laser’s absolute carrier phase for varying field strengths, frequencies, and pulse durations in order to verify the source of the probe laser absolute carrier-phase effect and to determine the conditions needed to most readily detect it.

A rotating-wave approximation (RWA) is developed to describe the interaction of a two-level system, which has permanent dipole moments, with two pulsed lasers. The RWA expressions for the time-dependent populations of the molecular states are applied to model laser-molecule interactions and tested by comparison with exact results. The results are used to discuss the pulsed-laser phase control of molecular excitation through the interplay of competing one- and two-photon resonances involving the effects of a nonzero difference *d* between the permanent dipoles of the two states involved in the transition; the competition vanishes if d=0.

Orientation and alignment parameters have been computed from first principles for the photodissociation of the HF and DF diatomic molecules. The calculations are entirely *ab initio*and the break-up dynamics of the molecule is treated rigorously taking account of the electronically nonadiabaticdynamics on three coupled adiabatic electronic potential energy curves. The potential energy curves and spin–orbit interactions, which have been previously reported [J. Chem. Phys. **113**, 1870 (2000)], are computed using *ab initio* molecular electronic structure computer codes. These are then used to compute photofragmentation **T** matrix elements using a time-dependent quantum mechanical wave packet treatment and from these a complete set of anisotropy parameters with rank up to K=3 is computed. The predicted vector correlations and alignment parameters are presented as a function of energy for HF and DF initially in both their ground and first excited vibrational states. The parameters predicted for the molecules which are initially in their excited vibrational states display a pronounced sharp energy dependence arising from the nodal structure of the initial vibrational wavefunction. The theoretical results are analyzed using a simple model of the dynamics and it is demonstrated how the magnitude and relative phases of the photofragmentation **T** matrix elements can be deduced from the experimentally measured alignment parameters. No experimental measurements have yet been made of alignment parameters for hydrogen halide diatomics and the present results provide the first predictions of these quantities which may be compared with future experimental observations.

We report a potential energy surface and calculations of power spectra for CH+5. The potential surface is obtained by precise fitting of MP2/cc-pVTZ electronic energies and gradients, which are obtained in classical direct-dynamics calculations. The power spectra are obtained using standard microcanonical classical and novel quasiclassical calculations of the velocity autocorrelation function, from which the power spectrum is obtained in the usual way. Both calculations agree qualitatively that the overall spectrum is quite complex; however, the latter calculations indicate that some spectral features may be assignable.

in Weakly Interacting Molecular Pairs: Unconventional Absorbers of Radiation in the Atmosphere, Proceedings of NATO Advanced Research Workshop, edited by C. Camy-Peret and A.A. Vigasin (Kluwer, The Netherlands, 2003), 93-99.

Publication year: 2003

The isomerization of acetylene to vinylidene is examined theoretically in full dimensionality (six degrees of freedom), using a new *ab initio*potential energy surface [S. Zou and J. M. Bowman, Chem. Phys. Lett. **368**, 421 (2003)]. Eigenfunctions and eigenvalues of the exact Hamiltonian, for zero total angular momentum, are obtained using a series of novel truncation/recoupling procedures that permits calculations up to very high energies. The Hamiltonian is given in diatom–diatom Jacobi coordinates, with the choice H2–C2 for the two diatoms in order to exploit the full permutational symmetry of the problem. By examining expectation values of the eigenfunctions, a number of states are definitely identified with vinylidenelike characteristics. Corresponding calculations are also done for C2D2. Full dimensional simulations of the photodetachment spectra of C2H−2 and C2D−2 are done (within the Franck–Condon approximation) and compared to the experimental ones. For this calculation the ground vibrational statewave function of the anion is obtained using a new force field, based on high quality *ab initio* calculations, which are also briefly reported.

We point out that normal modes and frequencies of molecules and molecular complexes can be obtained directly from a harmonically driven molecular dynamics calculation. We illustrate this approach for HOD and H5O+2 and then discuss its potential advantages over the standard Hessian-based approach for large molecules.

The production of spin-polarized hydrogen atoms from the photodissociation of hydrogen chloride with circularly polarized 193-nanometer light is inferred from the measurement of the complete angular momentum distributions of ground state Cl(^{2}P_{3/2})and excited state Cl(^{2}P_{1/2})cofragments by slice imaging. The experimentally measured and ab initio predicted (*p*)parameters, which describe the single-surface and multiple-surface-interference contributions to the angular momentum distributions, are in excellent agreement. For laser pulses longer than about 0.7 ns, the polarization of the electron and the proton are both 36%.

The translation-rotation collision-induced spectra of N_{2}–N_{2}, O_{2}–O_{2} and N_{2}–O_{2} mixtures are calculated theoretically. For N_{2}–N_{2}, using the matrix elements for the quadrupole and hexadecapole moments and the isotropic and anisotropic polarizabilities obtained previously from a global analysis of the fundamental band spectra, we obtain numerical values for the zeroth moment that are smaller than the measured values by 9–14%, depending on the temperature. By increasing the value for the matrix element of the isotropic polarizability slightly, good agreement with experiment is obtained. For O_{2}–O_{2}, the theoretical spectrum is significantly smaller than the experimental result. By increasing the matrix element of the hexadecapole moment by a factor of 1.7, we can obtain good agreement. This larger value for the hexadecapole moment will not appreciably affect the agreement found previously in the fundamental region because the hexadecapole contribution to the intensity is very small, unlike the translation-rotation band where it is larger than the contribution due to the quadrupole moment. Using these parameters, we then calculate the collision-induced absorption for N_{2}–O_{2} mixtures for which no experimental data exist. Finally, we calculate the collision-induced absorption for air, and compare our results with previous work; we express the results for the ratio of the absorption coefficient of air to that of N_{2}–N_{2} as a function of wavenumber and temperature,*R*(*ω*,*T*), which can easily be implemented in atmospheric models.

We report an ab initio calculation of the potential surface, quantum structures, and zero-point energies of CH5+ and CH2D3+ in full dimensionality. This potential energy surface is a very precise fit to 20 633 ab initio energies and an even larger data set of potential gradients, obtained at the MP2/cc-pVTZ level of theory/basis. The potential, which exactly obeys the permutational symmetry of the five hydrogen atoms, is used in diffusion Monte Carlo (DMC) calculations of the fully anharmonic zero-point energies and ground-state wave functions of CH5+ and CH2D3+. Bond length distributions are obtained from the DMC ground state and are compared to those resulting from classical molecular dynamics simulations, which are performed at the quantum zero-point energy for roughly 300 picoseconds.

The interaction of a two-level dipolar molecule with two laser pulses, where one laser’s frequency is tuned to the energy level separation (pump laser) while the second laser’s frequency is extremely small (probe laser), is investigated. A dipolar molecule is one with a nonzero difference between the permanent dipole moments of the molecular states. As shown previously [A. Brown, Phys. Rev. A 66, 053404 (2002)], the final population transfer between the two levels exhibits a dependence on the carrier-envelope phase of the probe laser. Based on the rotating-wave approximation (RWA), an effective Hamiltonian is derived to account for the basic characteristics of the carrier-envelope phase dependence effect. By analysis of the effective Hamiltonian, scaling properties of the system are found with regard to field strengths, pulse durations, and frequencies. According to these scaling properties, the final-state population transfer can be controlled by varying the carrier-envelope phase of the probe laser field using lasers with weak field strengths (low intensities) and relatively long pulse durations. In order to examine the possible roles of background states, the investigation is extended to a three-level model. It is demonstrated that the carrier-envelope phase effect still persists in a well-defined manner even when neighboring energy levels are present. These results illustrate the potential of utilizing excitation in dipolar molecules as a means of measuring the carrier-envelope phase of a laser pulse or if one can manipulate the carrier envelope phase, as a method of controlling population transfer in dipolar molecules. The results also suggest that the carrier-envelope phases must be taken into account properly when performing calculations involving pump-probe excitation schemes with laser frequencies which differ widely in magnitude.

The driven molecular-dynamics (DMD) method, recently proposed by Bowman, Zhang, and Brown [J. Chem. Phys. **119**, 646 (2003)], has been implemented into the TINKER molecular modeling program package. The DMD method yields frequencies and normal modes without evaluation of the Hessian matrix. It employs an external harmonic driving term that can be used to scan the spectrum and determine resonant absorptions. The molecular motions, induced by driving at resonant frequencies, correspond to the normal-mode vibrations. In the current work we apply the method to a 20-residue protein, Trp-cage, that has been reported by Neidigh, Fesinmeyer, and Andersen [Nature Struct. Biol. **9**, 425 (2002)]. The structural and dynamical properties of this molecule, such as *B*-factors, root-mean square fluctuations,anisotropies, vibrational entropy, and cross-correlations coefficients, are calculated using the DMD method. The results are in very good agreement with ones calculated using standard normal-mode analysis method. Thus, the DMD method provides a viable alternative to the standard Hessian-based method and has considerable potential for the study of large systems, where the Hessian-based method is not feasible.

The complete angular momentum distributions and vector correlation coefficients (orientation and alignment) of ground-state Cl(2P3/2) and excited-state Cl(2P1/2) atoms resulting from the photodissociation of HCl have been computed as a function of photolysis energy. Results for the corresponding H atom partner are also calculated and demonstrate that the H-atom produced is highly spin polarized. The theoretical results are determined using a time-dependent wave packet treatment of the dissociation dynamics based on ab initio potential energy curves, spin−orbit couplings, and dipole moments that have been reported previously [Alexander, M. H.; Pouilly, B.; Duhoo, T. *J. **Chem. Phys.* **1993**, *99*, 1752]. The theoretical orientation and alignment parameters, (p), that describe the coherent and incoherent contributions to the angular momentum distributions from the multiple dissociative states accessed by parallel and perpendicular transitions, are compared to experimental measurements made at 193 nm and excellent agreement is obtained. Theoretical predictions of the (p) parameters for the isotopically substituted species DCl, for which no experiments have yet been carried out, are reported and contrasted to the analogous HCl results. The results for the H atom spin polarizations are discussed in the context of three static models whose strengths and limitations are highlighted.

We report a full dimensional, *ab initio* based potential energy surface for CH+5. The *ab initio *electronic energies and gradients are obtained in direct-dynamics calculations using second-order Møller-Plesset perturbation theory with the correlation consistent polarized valence triple zeta basis. The potential energy and the dipole momentsurfaces are fit using novel procedures that ensure the full permutational symmetry of the system. The fitted potential energy surface is tested by comparing it against additional electronic energy calculations and by comparing normal mode frequencies at the three lowest-lying stationary points obtained from the fit against*ab initio* ones. Well-converged diffusion Monte Carlo zero-point energies,rotational constants, and projections along the CH and HH bond lengths and the tunneling coordinates are presented and compared with the corresponding harmonic oscillator and standard classical molecular dynamics ones. The delocalization of the wave function is analyzed through comparison of the CH+5 distributions with those obtained when all of the hydrogen atoms are replaced by 2H and 3H. The classical dipole correlation function is examined as a function of the total energy. This provides a further probe of the delocalization of CH+5.

in Theory of Chemical Reaction Dynamics, edited by A. Lagana and G. Lendvay (Kluwer Academic Publishers, Dordrecht, 2004), 145-189.

Publication year: 2004

Adiabatic potential energy surfaces for the six lowest singlet electronic states of N2O (X 1A′, 2 1A′, 3 1A′, 1 1A″, 2 1A″ and 3 1A″) have been computed using an *ab initio* multireference configuration interaction (MRCI) method and a large orbital basis set (aug-cc-pVQZ). The potential energy surfaces display several symmetry related and some nonsymmetry related conical intersections. Total photodissociation cross sections and product rotational state distributions have been calculated for the first ultraviolet absorption band of the system using the adiabatic *ab initio*potential energy and transition dipole momentsurfaces corresponding to the lowest three excited electronic states. In the Franck–Condon region the potential energy curves corresponding to these three states lie very close in energy and they all contribute to the absorption cross section in the first ultraviolet band. The total angular momentum is treated correctly in both the initial and final states. The total photodissociationspectra and product rotational distributions are determined for N2O initially in its ground vibrational state (0,0,0) and in the vibrationally excited (0,1,0) (bending) state. The resulting total absorption spectra are in good quantitative agreement with the experimental results over the region of the first ultraviolet absorption band, from 150 to 220 nm. All of the lowest three electronically excited states[1Σ−(1 1A″), 1Δ(2 1A′), and 1Δ(2 1A″)] have zero transition dipole moments from the ground state [1Σ+(1 1A′)] in its equilibrium linear configuration. The absorption becomes possible only through the bending motion of the molecule. The 1Δ(2 1A′)←X 1Σ+(1A′) absorption dominates the absorption cross section with absorption to the other two electronic states contributing to the shape and diffuse structure of the band. It is suggested that absorption to the bound 1Δ(2 1A″)state makes an important contribution to the experimentally observed diffuse structure in the first ultraviolet absorption band. The predicted product rotational quantum state distribution at 203 nm agrees well with experimental observations.

The complete angular momentum distributions and vector correlation coefficients (orientation and alignment) of ground stateI(2P3∕2) and excited stateI(P1∕22) atoms resulting from the photodissociation of HI have been computed as a function of photolysisenergy. The orientation and alignment parameters a(K)Q(p) that describe the coherent and incoherent contributions to the angular momentum distributions from the multiple electronic states accessed by parallel and perpendicular transitions are determined using a time-dependent wave packet treatment of the dissociation dynamics. The dynamics are based on potential energy curves and transition dipole moments that have been reported previously [R. J. LeRoy, G. T. Kraemer, and S. Manzhos, J. Chem. Phys.117, 9353 (2002)] and used to successfully model the scalar (total cross section and branching fraction) and lowest order vector (anisotropy parameter β) properties of the photodissociation. Predictions of the a(K)Q(p), parameters for the isotopically substituted species DI are reported and contrasted to the analogous HI results. The resulting polarization for the corresponding H/D partners are also determined and demonstrate that both H and D atoms produced can be highly spin polarized. Comparison of these predictions for HIand DI with experimental measurement will provide the most stringent test of the current model for the electronic structure and the interpretation of the dissociation based on noncoupled excited state dynamics.

Amplitudes and phases of the photofragmentation **T** matrix can be determined from experiment by measuring the vector correlation coefficients of the photofragments. Comparison of the experimentally obtained data with the results of quantum mechanical calculation allows the realization of the *complete experiment* in the field of molecular photodynamics. Selected studies where this analysis has been carried out are discussed.

in Normal Mode Analysis: Theory and Applications to Biological and Chemical Systems, edited by Q. Cui and I. Bahar, (CRC Press, 2006), pp.281-300.

Publication year: 2006

Ab initio potential energy curves, transition dipole moments, and spin−orbit coupling matrix elements are computed for HBr. These are then used, within the framework of time-dependent quantum-mechanical wave-packet calculations, to study the photodissociation dynamics of the molecule. Total and partial integral cross sections, the branching fraction for the formation of excited-state bromine atoms Br(2P1/2), and the lowest order anisotropy parameters, β, for both ground and excited-state bromine are calculated as a function of photolysis energy and compared to experimental and theoretical data determined previously. Higher order anisotropy parameters are computed for the first time for HBr and compared to recent experimental measurements. A new expression for the Re[ (∥, ⊥)] parameter describing coherent parallel and perpendicular production of ground-state bromine in terms of the dynamical functions is given. Although good agreement is obtained between the theoretical predictions and the experimental measurements, the discrepancies are analyzed to establish how improvements might be achieved. Insight is obtained into the nonadiabatic dynamics by comparing the results of diabatic and fully adiabatic calculations.

The photodissociation dynamics of HI and DI are examined using time-dependent wave-packet techniques. The orientation and alignment parameters a(K)Q(p) are determined as a function of photolysis energy for the resulting ground-stateI(2P3∕2) and excited-stateI(2P1∕2) atoms. The a(K)Q(p) parameters describe the coherent and incoherent contributions to the angular momentum distributions from the A1Π1, a1Π3, and t3Σ1 electronic states accessed by perpendicular excitation and the aΠ0+3 state accessed by a parallel transition. The outcomes of the dynamics based on both shifted *ab initio* results and three empirical models for the potential-energy curves and transitiondipole moments are compared and contrasted. It is demonstrated that experimental measurement of the a(K)Q(p) parameters for the excitation from the vibrational ground state(ʋ=0) would be able to distinguish between the available models for the HI potential-energy curves and transitiondipole moments. The differences between the a(K)Q(p)parameters for the excitation from ʋ=0 stand in sharp contrast to the scalar properties, i.e., total cross section and I∗ branching fraction, which require experimental measurement of photodissociation from excited vibrational states (ʋ>0) to distinguish between the models.

In this paper, a new method is proposed to design optimized control fields with desired temporal and/or spectral properties. The method is based on penalizing the difference between an optimized field obtained from an iterative scheme and a reference field with desired temporal and/or spectral properties. Compared with the standard optimal control theory, the current method allows a simple, experimentally accessible field be found on the fly; while compared with parameter space searching optimization, the iterative nature of this method allows automatic exploration of the intrinsic mechanism of the population transfer. The method is illustrated by examing the optimal control of vibrational excitation of the Cl–O bond with both temporally and spectrally restricted pulses.

In a recent paper [D. Babikov, J. Chem. Phys.121, 7577 (2004)], quantum optimal control theory was applied to analyze the accuracy of quantum gates in a quantum computer based on molecular vibrational eigenstates. The effects of the anharmonicity parameter of the molecule, the target time of the pulse, and the penalty function on the accuracy of the qubit transformations were investigated. We demonstrate that the effects of all the molecular and laser-pulse parameters can be explained utilizing the analytical pulse area theorem, which originates from the standard two-level model. Moreover, by analyzing the difference between the optimal control theory results and those obtained using the pulse area theorem, it is shown that extremely high quantum gate fidelity can be achieved for a qubit system based on vibrational eigenstates.

in Vector Correlation and Alignment in Chemistry, edited by G.G. Balint-Kurti and M.P. de Miranda (CCP6, Daresbury, 2006), pp.73-78.

Publication year: 2006

The effects of a background state, or states, on stimulated Raman adiabatic passage (STIRAP) processes are investigated. The study is based on a realistic model of the laser-assisted HCN→HNC isomerization process. While the high density of states in the energy regime above the isomerization barrier plays an important role, the strong variation of the transition dipole moments connecting these states with the localized HCN and HNC states is shown to be more significant in determining the success or failure of the STIRAP process. Therefore, care must be taken when proposing the use of STIRAP-based schemes to control molecular excitation especially when control is justified via few-level models.

The effects of permanent dipole moments on stimulated Raman adiabatic passage (STIRAP) are considered. Analytic expressions for the Hamiltonian including the effects of permanent dipole moments are developed for the STIRAP process. The potential detrimental effect of permanent dipoles on population transfer using standard STIRAP techniques is demonstrated using model three-level systems. However, the presence of permanent dipole moments can allow the utilization of alternative multi-photon mechanisms for STIRAP. Here two-photon plus two-photon STIRAP is highlighted as a potential new mechanism.

The assumption that the photodissociation of HI proceeds adiabatically is re-examined in the context of recently calculated alignment parameters, **a**(⟂), for the ground state halogen atoms resulting from photodissociation of the analogous HCl and HBr molecules. The **a**(⟂) alignment parameters for HCl, HBr, and HI are determined from time-dependent quantum mechanical wave packet calculations based on the best available ab initio electronic structure for each molecule. The experimental measurement of the alignment of the I(^{2}P_{3/2}) atoms is proposed as a stringent test of whether the photodissociation is adiabatic or involves non-adiabatic coupling of the *A*^{1}Π_{1} and a^{3}Π_{1}electronic states.

By virtue of its self-sufficiency to form a visible wavelength chromophore within the confines of its tertiary structure, the *Aequorea **victoria* green fluorescent protein (GFP) is single-handedly responsible for the ever-growing popularity of fluorescence imaging of recombinant fusion proteins in biological research. Engineered variants of GFP with altered excitation or emission wavelength maxima have helped to expand the range of applications of GFP. The engineering of the GFP variants is usually done empirically by genetic modifications of the chromophore structure and/or its environment in order to find variants with new photophysical properties. The process of identifying improved variants could be greatly facilitated if augmented or guided by computational studies of the chromophore ground and excited-state properties and dynamics. In pursuit of this goal, we now report a thorough investigation of computational methods for prediction of the absorbance maxima for an experimentally validated series of engineered GFP chromophore analogues. The experimental dataset is composed of absorption maxima for 10 chemically distinct GFP chromophore analogues, including a previously unreported Y66D variant, measured under identical denaturing conditions. For each chromophore analogue, excitation energies and oscillator strengths were calculated using configuration interaction with single excitations (CIS), CIS with perturbative correction for double substitutions [CIS(D)], and time-dependent density functional theory (TD DFT) using several density functionals with solvent effects included using a polarizable continuum model. Comparison of the experimental and computational results show generally poor quantitative agreement with all methods attempted. However, good linear correlations between the calculated and experimental excitation energies (*R*2>0.9) could be obtained. Oscillator strengths obtained with TD DFT using pure density functionals also correlate well with the experimental values. Interestingly, most of the computational methods used in this work fail in the case of nonaromatic Y66S and Y66L protein chromophores, which may be related to a significant contribution of double excitations to their excited-state wavefunctions. These results provide an important benchmark of the reliability of the computational methods as applied to GFP chromophore analogues and lays a foundation for the computational design of GFP variants with improved properties for use in biological imaging.

We have extended a previously implemented algorithm for using optimal control theory within the multi-configurational time-dependent Hartree (MCTDH) software. The new implementation allows the use of arbitrary dipole operators for generating the optimal laser field. A variant that does not require saving the time-dependent wave function has been developed, where simultaneous forward and backward propagations are performed. Input parameters are concentrated in a single input file analogous to the input files used elsewhere in MCTDH. We use here two simple examples to demonstrate the use of OCT-MCTDH: the modified Henon–Heiles potential and a two-dimensional model of acetylene. For both systems, a controlled transition between two vibrational states is tested. Results obtained with MCTDH and exact calculations are compared.

in Atoms and Molecules in Laser and External Fields, edited by M. Mohan (Narosa Publishing House, New Dehli, 2008), pp.51-58.

Publication year: 2008

The ground (X^{1}A′) and two lowest lying excited singlet states (1^{1}A″ and 2^{1}A′) of methyl hypochlorite have been examined using ab initio electronic structure techniques to validate computationally efficient methods, upon which direct dynamics can be based, versus high-level ones, for which direct dynamics would be intractable. Ground-state equilibrium geometries and vibrational frequencies determined using density functional theory (DFT) with the 6-31G(d) basis set are tested against coupled-cluster theory (CCSD(T)) results from the literature. Vertical excitation energies and transition dipole moments calculated at the complete active space self-consistent field CASSCF/6-31+G(d) level of theory are benchmarked against multireference configuration interaction (MRCI) results with the aug-cc-pV*X*Z (*X* = D, T, Q) family of basis sets. The excited-state gradients that will govern the classical dynamics are compared for CASSCF/6-31+G(d) versus MRCI/aug-cc-pV*X*Z (*X* = D, T). To carry out the ab initio molecular dynamics (AIMD), existing electronic structure codes have been interfaced with the molecular modelling toolkit (MMTK), an open-source program library for molecular simulation applications. We use two examples to demonstrate the use of direct dynamics in MMTK: a canonical ground-state trajectory to sample positions and momenta, and an excited-state microcanonical trajectory based on CASSCF. The work presented here forms the basis for future study of the photodissociation of CH_{3}OCl. As well, the implementation of AIMD within MMTK provides a useful tool for examining a variety of other research problems.

We present a modified version of a previously published algorithm (Gollub *et al* 2008 *Phys. Rev. Lett.***101** 073002) for obtaining an optimized laser field with more general restrictions on the search space of the optimal field. The modification leads to enforcement of the constraints on the optimal field while maintaining good convergence behaviour in most cases. We demonstrate the general applicability of the algorithm by imposing constraints on the temporal symmetry of the optimal fields. The temporal symmetry is used to reduce the number of transitions that have to be optimized for quantum gate operations that involve inversion (NOT gate) or partial inversion (Hadamard gate) of the qubits in a three-dimensional model of ammonia.

A scheme for coherent population transfer via four quantum states in atomic or molecular systems of high-energy transitions by induced multiphoton adiabatic passage (IMAP) is proposed. The nonperturbative multiphoton resonant theory of interaction of such quantum systems with the two strong laser fields of different frequencies is developed and the possibility of coherent control of population in high-energy quantum structures by IMAP is shown.

The photophysical properties of fluorochromes are directly influenced by their chemical structure. There is increasing interest in chemical strategies that provide controlled changes to the emission properties of biologically compatible fluorophores. One strategy employed is the conversion of a fluorophore-attached alkyne to a triazole through a copper-catalyzed Sharpless-Meldal reaction. In this study, we have examined a series of structurally related coumarin fluorophores and evaluated changes in their photophysical properties upon conversion from alkyne to triazole forms. Ethynyl-coumarin structures showed increases in quantum yield (ca. 1.2- to- 9 fold) and bathochromic shifts (up to 23 nm) after triazole formation. To extend these results, we tested the ability of time-dependent density functional theory (TD DFT) to predict the observed changes in fluorophore absorption properties. We found excellent correlation between the predicted absorption values and experiment, providing a useful tool in the design of new fluorogenic probes.

Comparative studies of implementations of the controlled NOTquantum gate operation using vibrational states of ammonia as the qubit states are presented. The quantum gate operations are realized using tailored laser pulses, which are calculated using a combined approach of optimal control theory and the multiconfiguration time-dependent Hartree method. We compare results obtained with a reduced model of ammonia with three degrees of freedom (all N–H bond distances fixed) to those obtained with a full six-dimensional model. In our study, the optimal laser pulses of both models induce similar underlying physical mechanisms while the gate quality within the reduced model (>98%) is much higher than within the six-dimensional model (≈80%).

Frequency domain shaped binary laser pulses were optimized to perform 2 qubitquantum gate operations in C12O16. The qubit rovibrational state representation was chosen so that all gate operations consisted of one-photon transitions. The amplitude and phase varied binary pulses were determined using a genetic algorithm optimization routine. Binary pulses have two possible amplitudes, 0 or 1, and two phases, 0 or π, for each frequency component of the pulse. Binary pulses are the simplest to shape experimentally and provide a minimum fidelity limit for amplitude and phase shaped pulses. With the current choice of qubit representation and using optimized binary pulses, fidelities of 0.80 and as high as 0.97 were achieved for the controlled-NOT and alternative controlled-NOT quantum gates. This indicates that with a judicious choice of qubits, most of the required control can be obtained with a binary pulse. Limited control was observed for 2 qubit NOT and Hadamard gates due to the need to control multiple excitations. The current choice of qubit representation produces pulses with decreased energies and superior fidelities when compared with rovibrational qubit representations consisting of two-photon transitions. The choice of input pulse energy is important and applying pulses of increased energy does not necessarily lead to a better fidelity.

We have demonstrated the use of *ab initio*molecular dynamics (AIMD) trajectories to compute the vibrational energy levels of molecular systems in the context of the semiclassical initial value representation (SC-IVR). A relatively low level of electronic structure theory (HF/3-21G) was used in this proof-of-principle study. Formaldehyde was used as a test case for the determination of accurate excited vibrational states. The AIMD-SC-IVR vibrational energies have been compared to those from curvilinear and rectilinear vibrational self-consistent field/vibrational configuration interaction with perturbation selected interactions-second-order perturbation theory (VSCF/VCIPSI-PT2) and correlation-corrected vibrational self-consistent field (cc-VSCF) methods. The survival amplitudes were obtained from selecting different reference wavefunctions using only a single set of molecular dynamics trajectories. We conclude that our approach is a further step in making the SC-IVR method a practical tool for first-principles quantum dynamics simulations.

The importance of the ro-vibrational state energies on the ability to produce high fidelity binary shaped laser pulses for quantum logic gates is investigated. The single frequency 2-qubit ACNOT_{1} and double frequency 2-qubit NOT_{2}quantum gates are used as test cases to examine this behaviour. A range of diatomics is sampled. The laser pulses are optimized using a genetic algorithm for binary (two amplitude and two phase parameter) variation on a discretized frequency spectrum. The resulting trends in the fidelities were attributed to the intrinsic molecular properties and not the choice of method: a discretized frequency spectrum with genetic algorithm optimization. This is verified by using other common laser pulse optimization methods (including iterative optimal control theory), which result in the same qualitative trends in fidelity. The results differ from other studies that used vibrational state energies only. Moreover, appropriate choice of diatomic (relative ro-vibrational state arrangement) is critical for producing high fidelity optimized quantum logic gates. It is also suggested that global phase alignment imposes a significant restriction on obtaining high fidelity regions within the parameter search space. Overall, this indicates a complexity in the ability to provide appropriate binary laser pulse control of diatomics for molecular quantum computing.

A fully quantum mechanical dynamical calculation on the photodissociation of molecular chlorine is presented. The magnitudes and phases of all the relevant photofragment *T*-matrices have been calculated, making this study the computational equivalent of a “complete experiment,” where all the possible parameters defining an experiment have been determined. The results are used to simulate cross-sections and angular momentumpolarization information which may be compared with experimental data. The calculations rigorously confirm the currently accepted mechanism for the UV photodissociation of Cl_{2}, in which the majority of the products exit on the C ^{1}Π_{1u }state, with non-adiabatic couplings to the A ^{3}Π_{1u }and several other Ω = 1 states, and a small contribution from the BΠ3 state present at longer wavelengths.

Deuterium kinetic isotope effects (KIEs) are reported for the first time for the dissociation of a protein–ligand complex in the gas phase. Temperature-dependent rate constants were measured for the loss of neutral ligand from the deprotonated ions of the 1:1 complex of bovine β-lactoglobulin (Lg) and palmitic acid (PA), (Lg + PA)*n*− → Lg*n*– + PA, at the 6– and 7– charge states. At 25 °C, partial or complete deuteration of the acyl chain of PA results in a measurable inverse KIE for both charge states. The magnitude of the KIEs is temperature dependent, and Arrhenius analysis of the rate constants reveals that deuteration of PA results in a decrease in activation energy. In contrast, there is no measurable deuterium KIE for the dissociation of the (Lg + PA) complex in aqueous solution at pH 8. Deuterium KIEs were calculated using conventional transition-state theory with an assumption of a late dissociative transition state (TS), in which the ligand is free of the binding pocket. The vibrational frequencies of deuterated and non-deuterated PA in the gas phase and in various solvents (*n*-hexane, 1-chlorohexane, acetone, and water) were established computationally. The KIEs calculated from the corresponding differences in zero-point energies account qualitatively for the observation of an inverse KIE but do not account for the magnitude of the KIEs nor their temperature dependence. It is proposed that the dissociation of the (Lg + PA) complex in aqueous solution also proceeds through a late TS in which the acyl chain is extensively hydrated such that there is no significant differential change in the vibrational frequencies along the reaction coordinate and, consequently, no significant KIE.

The effect of varying parameters specific to laser pulse shaping instruments on resulting fidelities for the ACNOT_{1}, NOT_{2}, and Hadamard_{2}quantum logic gates are studied for the diatomic molecule ^{12}C^{16}O. These parameters include varying the frequency resolution, adjusting the number of frequency components and also varying the amplitude and phase at each frequency component. A time domain analytic form of the original discretized frequency domain laser pulse function is derived, providing a useful means to infer the resulting pulse shape through variations to the aforementioned parameters. We show that amplitude variation at each frequency component is a crucial requirement for optimal laser pulse shaping, whereas phase variation provides minimal contribution. We also show that high fidelity laser pulses are dependent upon the frequency resolution and increasing the number of frequency components provides only a small incremental improvement to quantum gate fidelity. Analysis through use of the pulse area theorem confirms the resulting population dynamics for one or two frequency high fidelity laser pulses and implies similar dynamics for more complex laser pulse shapes. The ability to produce high fidelity laser pulses that provide both population control and global phase alignment is attributed greatly to the natural evolution phase alignment of the qubits involved within the quantum logic gate operation.

Velocity mapped ion imaging and resonantly enhanced multiphoton ionization time-of-flight methods have been used to investigate the photodissociation dynamics of the diatomic molecule Cl_{2} following excitation to the first UV absorption band. The experimental results presented here are compared with high level time dependent wavepacket calculations performed on a set of *ab initio* potential energy curves [D. B. Kokh, A. B. Alekseyev, and R. J. Buenker, J. Chem. Phys.120, 11549 (2004)10.1063/1.1753554]. The theoretical calculations provide the first determination of all dynamical information regarding the dissociation of a system of this complexity, including angular momentumpolarization. Both low rank *K* = 1, 2 and high rank *K* = 3 electronic polarization are predicted to be important for dissociation into both asymptotic product channels and, in general, good agreement is found between the recent theory and the measurements made here, which include the first experimental determination of high rank *K* = 3 orientation.

The nuclear quadrupole coupling constants (NQCCs) for the nitrogen and oxygen nuclei in N2O have been determined using a variety of computational methods (MP2, QCISD, DFT with B3LYP, PBE0, and B3PW91 functionals, CCSD, CCSD(T), CASSCF, and MRCI) combined with correlation-consistent basis sets. When compared to the available experimental determinations, the results demonstrate that only CCSD(T) and MRCI methods are capable of accurately predicting the NQCCs of the central and terminal nitrogen atoms. The spin-rotation and magnetic shielding tensors have also been determined and compared to experimental measurements where available. 14N and 17O NMR relaxation data for N2O in the gas phase and a variety of solvents is reported. The increase in the ratio of 14N spin–lattice relaxation times in solvent for the central and terminal nitrogens supports previous reports of the modification of the electric field gradients at these nuclei in van der Waals complexes. Ab initio computations for the linear FH···N2O complex confirm the large change in EFGs imposed by a single perturber.

General chemical strategies which provide controlled changes in the emission or absorption properties of biologically compatible fluorophores remain elusive. One strategy employed is the conversion of a fluorophore-attached alkyne (or azide) to a triazole through a copper-catalyzed azide–alkyne coupling (CuAAC) reaction. In this study, we have computationally examined a series of structurally related 2,1,3-benzoxadiazole (benzofurazan) fluorophores and evaluated changes in their photophysical properties upon conversion from alkyne (or azide) to triazole forms. We have also determined the photophysical properties for a known set of benzoxadiazole compounds. The absorption and emission energies have been determined computationally using time-dependent density functional theory (TD-DFT) with the Perdew, Burke, and Ernzerhof exchange-correlation density functional (PBE0) and the 6-31+G(d) basis set. The TD-DFT results consistently agreed with the experimentally determined absorption and emission wavelengths except for certain compounds where charge-transfer excited states occurred. In addition to determining the absorption and emission wavelengths, simple methods for predicting relative quantum yields previously derived from semiempirical calculations were reevaluated on the basis of the new TD-DFT results and shown to be deficient. These results provide a necessary framework for the design of new substituted benzoxadiazole fluorophores.

The photodissociation of vibrationally excited Cl_{2}(*v* = 1) has been investigated experimentally using the velocity mapped ion imaging technique. The experimental measurements presented here are compared with the results of time-dependent wavepacket calculations performed on a set of *ab initio* potential energy curves. The high level calculations allow prediction of all the dynamical information regarding the dissociation, including electronic polarization effects. Using a combination of theory and experiment it was found that there was negligible cooling of the vibrational degree of freedom of the parent molecule in the molecular beam. The results presented are compared with those following the photodissociation of Cl_{2}(*v* = 0). Although the same electronic states are found to be important for Cl_{2}(*v* = 1) as for Cl_{2}(*v* = 0), significant differences were found regarding many of the observables. The overall level of agreement between theory and experiment was found to be reasonable and confirms previous assignments of the photodissociation mechanism.

The ground state potential energy and dipole moment surfaces for CS2 have been determined at the CASPT2/C:cc-pVTZ,S:aug-cc-pV(T+d)Z level of theory. The potential energy surface has been fit to a sum-of-products form using the neural network method with exponential neurons. A generic interface between neural network potential energy surface fitting and the Heidelberg MCTDH software package is demonstrated. The potential energy surface has also been fit using the *potfit* procedure in MCTDH. For fits to the low-energy regions of the potential, the neural network method requires fewer parameters than *potfit* to achieve high accuracy; global fits are comparable between the two methods. Using these potential energy surfaces, the vibrational energies have been computed for the four most abundant CS2 isotopomers. These results are compared to experimental and previous theoretical data. The current potential energy surfaces are shown to accurately reproduce the low-lying vibrational energies within a few wavenumbers. Hence, the potential energy and dipole moments surfaces will be useful for future study on the control of quantum dynamics in CS2.

The stability of a variety of borane (BH3 and BH2NHMe) and silane (SiH*n*Ph4–*n*, *n* = 0–4) adducts with diamino (NHC) and aminoalkyl (CAAC) carbenes has been carefully examined using M06-2X/cc-pVDZ computations, including natural bond orbital and atoms-in-molecules analyses. Moreover a potential mechanism for the hydride-mediated ring expansion of the carbene donors is reported. While the NHC adducts can undergo thermally induced ring-expansion chemistry, the CAAC adducts show increased stability due to a large energetic barrier for the insertion of boron (or silicon) atoms into the CAAC heterocycle. A series of substituted NHCs were investigated to further explore the roles of both electronic and steric effects on adduct stabilities and on their propensities for undergoing ring-expansion transformations.

In this work, we present time dependent density functional theory (TD-DFT) computations of the photophysical properties for a recently synthesized family of emissive RNA nucleobases (see: D. Shin, R.W. Sinkeldam, Y. Tor, Journal of the American Chemical Society 133 (2011) 14912–14915). These modified analogues are obtained by replacing the imidazole moiety of the RNA nucleobases with thiopene and represent a complete alphabet of emissive and isomorphic analogues derived from one heterocylic nucleus. An extensive study of absorption and emission wavelengths as well as the excited state charge transfer character for these molecules was conducted at the TD-DFT/6-311++G(2df,2p) level of theory employing the CAM-B3LYP, B3LYP and PBE0 functionals in water and dioxane. The theoretical results reveal good agreement with the reported experimental data. The nature of the low-lying excited states are compared and contrasted with their naturally occurring RNA nucleobase counterparts.

**To branch or not to branch**: A mild stepwise route to various linear and branched (GeCl_{2})_{x} oligogermylenes supported by Lewis bases is reported, including the carbene-bound Ge_{4} complex NHC⋅GeCl_{2}Ge(GeCl_{3})_{2} (see picture). Dipp=2,6-*i*Pr_{2}C_{6}H_{3}, NHC=N-heterocyclic carbene.

The nuclear quadrupole coupling and spin-rotation constants of aluminum in AlH and AlD have been determined using coupled cluster theory with single and double excitations as well as perturbative inclusion of triples [CCSD(T)] combined with large correlation-consistent basis sets, cc-pCVXZ (X = T, Q and 5) and aug-cc-pCVXZ (X = T, Q). The anharmonic vibrational frequencies have been computed using second-order vibrational perturbation theory and the effects of vibrational averaging on the hyperfine constants have been determined. The ground state dipole moment has been determined for both isotopologues (AlH and AlD) and shown to depend critically on vibrational averaging. For completeness, the isotropic and anisotropic nuclear magnetic shielding tensors are also reported. All the results agree well with the best available experimental measurements, and in some cases (spin-rotation constants and dipole moments) refine the known data. The present computational results for the vibrationally averaged electric field gradients suggest that the currently accepted nuclear quadruple moment for ^{27}Al of may be slightly underestimated. Based on the experimental measurements of the nuclear quadrupole coupling for AlH (AlD) and best computational determinations of the vibrationally averaged electric field gradients, the quadruple moment of ^{27}Al is determined to be . However, this conclusion would be further strengthened with more precise experimental measurement of the ^{27}Al nuclear quadrupole coupling for AlH and AlD.

The elusive parent inorganic ethylene H2GeGeH2 has been isolated in the form of a stable complex for the first time via donor–acceptor coordination with suitable Lewis base/acid combinations (LB·H2Ge-GeH2·LA; LB = N-heterocyclic carbene or N-heterocyclic olefin; LA = W(CO)5). The nature of the bonding in these species was investigated by density functional theory calculations and revealed the presence of polarized Ge–Ge covalent σ-bonds within the H2Ge–GeH2 arrays and dative Ge–C interactions between the digermene and the carbon-based Lewis bases.

We present isolable examples of formal zinc hydride cations supported by N-heterocyclic carbene (NHC) donors, and investigate the dual electrophilic and nucleophilic (hydridic) character of the encapsulated [ZnH]^{+} units by computational methods and preliminary hydrosilylation catalysis.

The synthesis of the first examples of tellurophenes exhibiting phosphorescence in the solid state and under ambient conditions (room temperature and in air) is reported. Each of these main-group-element-based emitters feature pinacolboronates (BPin) as ring-appended side groups. The nature of the luminescence observed was also investigated using computational methods.

We present a computational study on HIO2 molecules. Ground state properties such as equilibrium structures, relative energetics, vibrational frequencies, and infrared intensities were obtained for all the isomers at the coupled-cluster with single and double excitations as well as perturbative inclusion of triples (CCSD(T)) level of theory with the aug-cc-pVTZ-PP basis set and ECP-28-PP effective core potential for iodine and the aug-cc-pVTZ basis set for hydrogen and oxygen atoms. The HOIO structure is confirmed as the lowest energy isomer. The relativeenergies are shown to be HOIO < HOOI < HI(O)O. The HO(O)I isomer is only stable at the density functional theory (DFT) level of theory. The transition states determined show interconversion of the isomers is possible. In order to facilitate future experimental identification, vibrational frequencies are also determined for all corresponding deuterated species. Verticalexcitation energies for the three lowest-lying singlet and triplet excited states were determined using the configuration interaction singles, time-dependent density functional theory (TD-DFT)/B3LYP, TD-DFT/G96PW91, and equation of motion-CCSD approaches with the LANL2DZ basis set plus effective core potential for iodine and the aug-cc-pVTZ basis set for hydrogen and oxygen atoms. It is shown that HOIO and HOOI isomers have excited states accessible at solar wavelengths (<4.0 eV) but these states have very small oscillator strengths (<2 × 10^{−3}).

The resonance Raman spectrum of uracil is simulated using the Herzberg–Teller short-time dynamics formalism. The ground-state geometry is optimized at the levels of PBE0/aug-cc-pVTZ and B3LYP/aug-cc-pVTZ, respectively. The gradient of the bright excited state is computed using time-dependent density functional theory and spin-flip time-dependent density functional theory. The excited-state calculations are carried out in both the gas phase and implicit water using the conductor-like polarizable continuum model. The ground-state equilibrium structure is found to impact the resulting resonance Raman spectrum significantly. The simulated resonance Raman spectrum using the long-range corrected functionals, that is, CAMB3LYP and LC-BLYP, and based on the PBE0/aug-cc-pVTZ optimized ground-state structure shows better agreement with the experimental spectrum than using standard hybrid functionals, that is, PBE0 and B3LYP. The solvation effect leads to a change in the energetic order of the *n* → π* and π → π* excited states, and it improves the agreement with the experimental spectrum, especially with regard to the relative intensities of the peaks with frequencies greater than 1600 cm–1.

in Molecular Quantum Dynamics: From Theory to Applications (Physical Chemistry in Action), edited by F. Gatti (Springer, Berlin, 2014), pp. 249-270.

Publication year: 2014

Two-photon spectroscopy of fluorescent proteins is a powerful bioimaging tool. Considerable effort has been made to measure absolute two-photon absorption (TPA) for the available fluorescent proteins. Being a technically involved procedure, there is significant variation in the published experimental measurements even for the same protein. In this work, we present a time-dependent density functional theory (TDDFT) study on isolated chromophores comparing the ability of four functionals (PBE0, B3LYP, CAM-B3LYP, and LC-BLYP) combined with the 6-31+G(d,p) basis set to reproduce averaged experimental TPA energies and cross sections. The TDDFT energies and TPA cross sections are also compared to corresponding CC2/6-31+G(d,p) results for excitation to S1 for the five smallest chromophores. In general, the computed TPA energies are less functional dependent than the TPA cross sections. The variation between functionals is more pronounced when higher-energy transitions are studied. Changes to the conformation of a chromophore are shown to change the TPA cross-section considerably. This adds to the difficulty of comparing an isolated chromophore to the one embedded in the protein environment. All functionals considered give moderate agreement with the corresponding CC2 results; in general, the TPA cross sections determined by TDDFT are 1.5–10 times smaller than the corresponding CC2 values for excitation to S1. LC-BLYP and CAM-B3LYP give erroneously large TPA cross sections in the higher-energy regions. On the other hand, B3LYP and PBE0 yield values that are of the same order of magnitude and in some cases very close to the averaged experimental data. Thus, based on the results reported here, B3LYP and PBE0 are the preferred functionals for screening chromphores for TPA. However, at best, TDDFT can be used to semiquantitatively scan chromophores for potential TPA probes and highlight spectroscopic peaks that could be present in the mature protein.

The stability of a variety of linear and cyclic (BN)n (n = 1–3) adducts with N-heterocyclic carbene (ImMe2; ImMe2 = [(HCNMe)2C:]), N-heterocyclic olefin (ImMe2CH2) and Wittig (Me3PCH2) donors has been examined using M05-2X/cc-pVTZ computations. The strength and nature of the bonds have been investigated using natural bond orbital (NBO) and atoms- in-molecules (AIM) analyses. Complementary energy decomposition analysis (EDA-NOCV) has been carried out based on BP86/TZ2P computations. In agreement with NBO and AIM analyses, the orbital interaction energy obtained from EDA con- tributes at least 50% to the total attractive interactions for the carbon–boron bonds indicating their largely covalent nature. The feasibility of isolating monomeric (BN)n units using a donor/acceptor protocol was also investigated in a series of adducts of the general form: LB·(BN)n·BH3 and LB·(BN)n·W(CO)5 (n = 1-3; LB = Lewis bases). Moreover, EDA-NOCV analysis of ImMe2·BN·W(CO)5 and ImMe2·B3N3·W(CO)5 shows that the carbene–boron bonds are stronger in the presence of W(CO)5 as a Lewis acid mainly because of a dramatic decrease in the amount of Pauli repulsion rather than an increase in the electro- static/orbital attraction terms.

The zirconium-mediated syntheses of pinacolboronate (BPin) appended benzo[*b*]tellurophenes and two phenyl/BPin substituted tellurophene isomers with different colors of emission have been achieved. These species are new additions to an emerging class of inorganic heterocycles that display visible phosphorescence in the solid state under ambient conditions.

The resonance Raman spectra of the 5-halogenated (F, Cl, and Br) uracils are simulated via the Herzberg-Teller (HT) short-time dynamics formalism. The gradient of the S_{1} excited state is computed at the CAMB3LYP/aug-cc-pVTZ level of theory in the conductor-like Polarizable Continuum Model for water (C-PCM, H_{2}O}), based on the equilibrium geometry determined using PBE0/aug-cc-pVTZ in H_{2}O (C-PCM). The simulated resonance Raman spectra show good agreement with the experimental spectra both in terms of peak positions and intensities. The differences between the resonance Raman spectra of the three 5-halogenated uracils, caused by the effect of halogen substitution, are examined in terms of ground state normal mode eigenvectors and excited state Cartesian gradients, according to the HT formalism. The differences in the normal mode eigenvectors and excited state Cartesian gradients between 5-fluorouracil and 5-chlorouracil are used to interpret the dissimilarity between their resonance Raman spectra. Meanwhile, the similarity between the spectra of 5-chlorouracil and 5-bromouracil is explained by the correspondence between their normal modes and excited state gradients.

Two-photon spectroscopy of fluorescent proteins is a powerful bio-imaging tool characterized by deep tissue penetration and little damage. However, two-photon spectroscopy has lower sensitivity than one-photon microscopy alternatives and hence a protein with a large two-photon absorption cross-section is needed. We use time-dependent density functional theory (TD-DFT) at the B3LYP/6-31+G(d,p) level of theory to screen twenty-two possible chromophores that can be formed upon replacing the amino-acid Tyr66 that forms the green fluorescent protein (GFP) chromophore with a non-canonical amino acid. A proposed chromophore with a nitro substituent was found to have a large two-photon absorption cross-section (29 GM) compared to other fluorescent protein chromophores as determined at the same level of theory. Classical molecular dynamics are then performed on a nitro-modified fluorescent protein to test its stability and study the effect of the conformational flexibility of the chromophore on its two-photon absorption cross-section. The theoretical results show that the large cross-section is primarily due to the difference between the permanent dipole moments of the excited and ground states of the nitro-modified chromophore. This large difference is maintained through the various conformations assumed by the chromophore in the protein cavity. The nitro-derived protein appears to be very promising as a two-photon absorption probe.

The vertical excitation energies of 17 boron-dipyrromethene (BODIPY) core structures with a variety of substituents and ring sizes are benchmarked using time-dependent density functional theory (TD-DFT) with nine different functionals combined with the cc-pVTZ basis set. When compared to experimental measurements, all functionals provide mean absolute errors (Mean AEs) greater than 0.3 eV; larger than the 0.1-0.3 eV differences typically expected from TD-DFT. Due to the high linear correlation of TD-DFT results with experiment, most functionals can be used to predict excitation energies if corrected empirically. Using the CAM–B3LYP functional, 0-0 transition energies are determined and, while the absolute difference is improved (Mean AE = 0.478 eV compared to 0.579 eV), the correlation diminishes substantially (R^{2} of 0.961 to 0.862). Two very recently introduced charge transfer (CT) indices, q_{CT} and d_{CT}, and electron density difference (EDD) plots demonstrate that CT does not play a significant role for most of the BODIPYs examined, and, thus cannot be the source of error in TD-DFT. Therefore, vertical excitation energies are determined utilizing TD-HF, configuration interaction CIS and CIS(D), equation of motion EOM-CCSD, SAC-CI, and Laplace-transform based local coupled-cluster singles and doubles LCC2* methods. Moreover, multi-reference CASSCF and CASPT2 vertical excitation energies were also obtained for all species (except CASPT2 was not feasible for the 4 largest systems). The SAC-CI/cc-pVDZ, LCC2*/cc-pVDZ, and CASPT2/cc-pVDZ approaches are shown to have the smallest Mean AEs of 0.154 eV, 0.109 eV, and 0.100 eV, respectively; the utility of the LCC2* approach is demonstrated for 8 extended BODIPYs and aza-BODIPYs. The problems with TD-DFT arise from difficulties in dealing with the differential electron correlation (as assessed by comparing CCS, CC2, LR-CCSD, CCSDR(T), and CCSDR(3) vertical excitation energies for 5 compounds) and from contributions of multi-reference character and double excitations (from analysis of the CASSCF wave functions).

We present a computational study on two flavonols that were recently isolated from Loranthaceae family plant extracts: kaempferol 3-*O*-*α*-*L*-arabinofuranosyl-(1 → 3)-*α*-*L*-rhamnoside and quercetin 3-*O*-*α*-*L*-arabinofuranosyl-(1 → 3)-*α*-*L*-rhamnoside. Their structures and energetics have been investigated at the density functional level of theory, up to B3LYP/6-31+G(d,p), incorporating solvent effects with polarizable continuum models. In addition, their potential antioxidant activities were probed through the computation of the (i) bond dissociation enthalpies (BDEs), which are related to the hydrogen-atom transfer mechanism (HAT), and (ii) ionization potentials (IPs), which are related to the single-electron transfer mechanism (SET). The BDEs were determined in water to be 83.23 kcal/mol for kaempferol 3-*O*-*α*-*L*-arabinofuranosyl-(1 → 3)-*α*-*L*-rhamnoside and 77.49 kcal/mol for quercetin 3-*O*-*α*-*L*-arabinofuranosyl-(1 → 3)-*α*-*L*-rhamnoside. The corresponding IPs were obtained for both compounds as 133.38 and 130.99 kcal/mol, respectively. The BDEs and IPs are comparable to those probed for their parental molecules kaempferol and quercetin; this is in marked contrast to previous studies where glycosylation at the 3-position increases the corresponding BDEs, and, hence, decreases subsequent antioxidant activity. The BDEs and IPs obtained suggest both compounds are promising for antioxidant activity and thus further experimental tests are encouraged.

(BODIPY) dimers is carefully examined by means of ab initio and

Tamm−Dancoff approximated density functional theory meth-

ods. Vertical and 0−0 excitation energies along with the

tetraradical character of these dimers are determined. Possible

application of a series of linked dimers for photodynamic therapy

(PDT) was investigated through computing their excitation

energies, spin−orbit coupling matrix elements, and singlet−triplet

energy gaps. Finally through a systematic investigation of a series of 36 different BODIPY and aza-BODIPY dimers, a new class of near-IR heavy atom free photosensitizers for PDT action is introduced.

We have constructed a (semi)-global six-dimensional potential energy surface (PES) for HFCO, incorporating the equilibrium, cis- and trans-isomers (HOCF) as well as the transition states connecting them. The PES is based on a fit to 15000 CCSD(T)-F12/cc-pVTZ-F12 ab initio energies. The sum-of-products PES, obtained using neural network exponential fitting functions, was used to compute vibrational state frequencies using block improved relaxation with the multiconfiguration time dependent Hartree (MCTDH) approach. The PES is accurate (RMSE = 130 cm^{-1}) up to 40000 cm^{-1} above the minimum energy. The equilibrium region of the PES was fit very well based on a comparison of the vibrational frequencies with those from a recent local HFCO PES [J. Chem. Phys. 144, 174305 (2016)] and experimental measurements (RMSE = 10.9 cm^{-1} compared to experiment). The vibrational frequencies for the trans- and cis-isomers are computed from the PES and compared to anharmonic MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ results; the trans-and cis-isomers have yet to be detected experimentally. Based on the accuracy of the vibrational energies at equilibrium, the present results for the cis- and trans-isomers could facilitate the identification of these species. The PES will also enable the study of intramolecular vibrational energy redistribution and its control leading to the elusive equilibrium to trans-conversion.

Two-photon spectroscopy of fluorescent proteins is a powerful bio-imaging tool known for deep tissue penetration and little cellular damage. Being less sensitive than the one-photon microscopy alternatives, a protein with a large two-photon absorption (TPA) cross-section is needed. Here, we use time-dependent density functional theory (TD-DFT) at the B3LYP and CAM-B3LYP/6-31+G(d,p) levels of theory to screen twenty-two possible chromophores that can be formed upon replacing the amino-acid Tyr66 that forms the red fluorescent protein (RFP) chromophore with a non-canonical amino acid. The two-level model for TPA was used to assess the properties (i.e., transition dipole moment, permanent dipole moment difference, and the angle between them) leading to the TPA cross-sections determined via response theory. Computing TPA cross-sections with B3LYP and CAM-B3LYP yield similar overall trends. Results using both functionals agree that the RFP-derived model of the Gold Fluorescent Protein chromophore (Model 20) has the largest intrinsic TPA cross-section. TPA was further computed for selected chromophores following conformational changes: variation of both the dihedral angle of the acylimine moiety and the tilt and twist angles between the rings of the chromophore. The TPA cross-section assumed an oscillatory trend with the rotation of the acylimine dihedral, and the TPA is maximized in the planar conformation for almost all models. Model 21 (a hydroxyquinoline derivative) is shown to be comparable to model 20 in terms of TPA cross-section. The conformational study on Model 21 shows that the acylimine angle has a much stronger effect on the TPA than its tilt and twist angles. Having an intrinsic TPA ability that is more than 7 times that of the native RFP chromophore, Models 20 and 21 appear to be very promising for future experimental investigation.

The HBrO_{2} isomers have been analyzed computationally to confirm the previous experimental assignments for HOOBr and HOBrO, and to assist in future identification of the as yet unobserved HBr(O)O isomer. Optimized geometries of the HOOBr, HOBrO and HBr(O)O isomers and the transition states connecting them were obtained at the CCSD(T)/O, H: aug-cc-pVTZ, Br: aug-cc-pVTZ-PP level of theory. The corresponding harmonic vibrational frequencies for the HOOBr, HOBrO and HBr(O)O isomers are reported for all isotopologues considered in the experimental measurements, i.e., those involving hydrogen, deuterium, ^{79}Br, ^{81}Br, ^{16}O, and ^{18}O. The relative energetics of the stationary point geometries were determined through extrapolation of energies to the complete basis set limit. To explain the photodestruction observed experimentally for HOOBr and HOBrO, the three lowest low-lying singlet and triplet excited electronic states for each of the three isomers were computed using the equation-of-motion coupled-cluster with inclusion of single and double excitations (EOM-CCSD) and time-dependent density functional theory (TD-B3LYP and TD-CAM-B3LYP) approaches; all utilizing the all-electron aug-cc-pVTZ basis sets for all atoms. Multi-reference configuration interaction (MRCI)/aug-cc-pVTZ computations were carried out for the lowest singlet and lowest two triplet excited states. The vertical excitation energies for the low-lying excited states of the most stable isomer (HOOBr) are reported for the first time. The vibrational frequencies for the HBrO_{2} isomers are used along with new anharmonic vibrational frequency computations (at the PBE0/aug-cc-pVTZ level of theory) and vertical excitation energies (at the TD-B3LYP/aug-cc-pVTZ, TD-CAMB3LYP/aug-cc-pVTZ, and EOM-CCSD/aug-cc-pVTZ levels of theory) for the HBrO_{3} isomers, HOOOBr and HOOBrO, to determine that previously unassigned peaks in the experimental spectrum generated from HBr/O_{2} photolysis in a Ne-matrix belong to HOOOBr.

Two-photon absorption (TPA) leads to higher-energy excited electronic states via the simultaneous absorption of two photons. In TPA, the absorption is directly proportional to the square of incident light intensity, and thus lasers are required for excitation. The advantages of TPA microscopy include better focus and less out-of-focus bleaching, together with absorption at longer wavelengths than in one-photon absorption, which leads to deeper penetration in scattering media, such as tissues. However, TPA probes are usually associated with less sensitivity, and thus designing TPA fluorophores with large absorption probability is an important area of research. TPA of biological molecules like fluorescent proteins and nucleic acids is of particular interest. These molecules are experimentally produced through utilization of the naturally present transcription mechanism in the cell and thus pose less cell toxicity. In this chapter, we review the theory of TPA highlighting the computational approaches used to study biological molecules. We discuss the computational methods available for exploring TPA and recent computational studies on the TPA of fluorescent proteins and nucleic acid base analogues. The chapter concludes by highlighting possible research avenues and unanswered questions.

A six-dimensional potential energy surface (PES) for formyl fluoride (HFCO) is fit in a sum-of-products form using neural network exponential fitting functions. The ab initio data upon which the fit is based were computed at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations [CCSD(T)-F12]/cc-pVTZ-F12 level of theory. The PES fit is accurate (RMSE = 10 cm−1) up to 10 000 cm−1 above the zero point energy and covers most of the experimentally measured IR data. The PES is validated by computing vibrational energies for both HFCO and deuterated formyl fluoride (DFCO) using block improved relaxation with the multi-configuration time dependent Hartree approach. The frequencies of the fundamental modes, and all other vibrational states up to 5000 cm−1 above the zero-point energy, are more accurate than those obtained from the previous MP2-based PES. The vibrational frequencies obtained on the PES are compared to anharmonic frequencies at the MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels of theory obtained using second-order vibrational perturbation theory. The new PES will be useful for quantum dynamics simulations for both HFCO and DFCO, e.g., studies of intramolecular vibrational redistribution leading to unimolecular dissociation and its laser control.