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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.

2005-2009Book Chapters

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

2005-2009Journal Article

J. Phys. Chem. A 110, 5371-5378 (2006). [John C. Light Festschrift]

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.

2005-2009Book Chapters

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.

2005-2009Journal Article

Int. J. Quant. Chem. 107 2665-2671 (2007). [Special Issue on 11th European Workshop on Quantum systems in Chemistry and Physics (QSCP-11), St. Petersburg, Russia]

Publication year: 2007

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.

2005-2009Book Chapters

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

2005-2009Journal Article

Can. J. Chem. 87 1022-1029 (2009). [Ziegler special Issue]

Publication year: 2009

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.

2005-2009Journal Article

New J. Phys. 11 105031 (2009). [Quantum control special issue]

Publication year: 2009

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%).