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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).

2000-2004Conference Proceedings

in Proceedings of the 15th International Conference on Spectral Line Shapes, edited by J. Seidel (AIP, New York, 2001), Vol. 11, 436-438.

Publication year: 2001

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}).

2000-2004Book Chapters

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.

2000-2004Conference Proceedings

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%.

2000-2004Journal Article

Journal of Quantitative Spectroscopy and Radiative Transfer 82,505-516 (2003).

Publication year: 2003

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.

2000-2004Journal Article

J. Phys. Chem. A 108, 7790-7800 (2004). [Richard Bersohn Memorial Issue]

Publication year: 2004

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.

2000-2004Book Chapters

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

Publication year: 2004