Electronic Absorption and Resonance Raman Spectroscopy from Ab Initio Quantum Molecular Dynamics

Photo-induced structural dynamics of o-nitrophenol by ultrafast electron diffraction

The photo-induced dynamics of o-nitrophenol, particularly its photolysis, has garnered significant scientific interest as a potential source of nitrous acid in the atmosphere. Although the photolysis products and preceding photo-induced electronic structure dynamics have been investigated extensively, the nuclear dynamics accompanying the non-radiative relaxation of o-nitrophenol on the ultrafast timescale, which include an intramolecular proton transfer step, have not been experimentally resolved. Herein, we present a direct observation of the ultrafast nuclear motions mediating photo-relaxation using ultrafast electron diffraction. This work spatiotemporally resolves the loss of planarity which enables access to a conical intersection between the first excited state and the ground state after the proton transfer step, on the femtosecond timescale and with sub-Angstrom resolution. Our observations, supported by ab initio multiple spawning simulations, provide new insights into the proton transfer mediated relaxation mechanism in o-nitrophenol.

Finite-temperature vibronic spectra from the split-operator coherence thermofield dynamics

We present a numerically exact approach for evaluating vibrationally resolved electronic spectra at finite temperatures using the coherence thermofield dynamics. In this method, which avoids implementing an algorithm for solving the von Neumann equation for coherence, the thermal vibrational ensemble is first mapped to a pure-state wavepacket in an augmented space, and this wavepacket is then propagated by solving the standard, zero-temperature Schrödinger equation with the split-operator Fourier method. We show that the finite-temperature spectra obtained with the coherence thermofield dynamics in a Morse potential agree exactly with those computed by Boltzmann-averaging the spectra of individual vibrational levels. Because the split-operator thermofield dynamics on a full tensor-product grid is restricted to low-dimensional systems, we briefly discuss how the accessible dimensionality can be increased by various techniques developed for the zero-temperature split-operator Fourier method.

Calculating Multidimensional Optical Spectra from Classical Trajectories

Multidimensional optical spectra are measured from the response of a material system to a sequence of laser pulses and have the capacity to elucidate specific molecular interactions and dynamics whose influences are absent or obscured in a conventional linear absorption spectrum. Interpretation of complex spectra is supported by theoretical modeling of the spectroscopic observable, requiring implementation of quantum dynamics for coupled electrons and nuclei. Performing numerically correct quantum dynamics in this context may pose computational challenges, particularly in the condensed phase. Semiclassical methods based on calculating classical trajectories offer a practical alternative. Here I review the recent application of some semiclassical, trajectory-based methods to nonlinear molecular vibrational and electronic spectra.

Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Multi-configuration electron-nuclear dynamics: An open-shell approach

The multi-configuration electron-nuclear dynamics for open shell systems with a spin-unrestricted formalism is described. The mean fields are evaluated using second-order reduced density matrices for electronic and nuclear degrees of freedom. Applications to light-element diatomics including equilibrium geometries, electronic energies, dipole moments, and absorption spectra are presented. The von Neumann entropies for different spin states of a LiH molecule are compared.

On-the-fly ab initio semiclassical evaluation of vibronic spectra at finite temperature

To compute and analyze vibrationally resolved electronic spectra at zero temperature, we have recently implemented the on-the-fly ab initio extended thawed Gaussian approximation [A. Patoz et al., J. Phys. Chem. Lett. 9, 2367 (2018)], which accounts for anharmonicity, mode-mode coupling, and Herzberg-Teller effects. Here, we generalize this method in order to evaluate spectra at non-zero temperature. In line with thermo-field dynamics, we transform the von Neumann evolution of the coherence component of the density matrix to the Schrödinger evolution of a wavefunction in an augmented space with twice as many degrees of freedom. Due to the efficiency of the extended thawed Gaussian approximation, this increase in the number of coordinates results in nearly no additional computational cost. More specifically, compared to the original, zero-temperature approach, the finite-temperature method requires no additional ab initio electronic structure calculations. At the same time, the new approach allows for a clear distinction among finite-temperature, anharmonicity, and Herzberg-Teller effects on spectra. We show, on a model Morse system, the advantages of the finite-temperature thawed Gaussian approximation over the commonly used global harmonic methods and apply it to evaluate the symmetry-forbidden absorption spectrum of benzene, where all of the aforementioned effects contribute.

The 3s Rydberg state as a doorway state in the ultrafast dynamics of 1,1-difluoroethylene

The deactivation dynamics of 1,1-difluoroethylene after light excitation is studied within the surface hopping formalism in the presence of 3s and 3p Rydberg states using multi-state second order perturbation theory (MS-CASPT2).

Time-Dependent Formulation of Resonance Raman Optical Activity Spectroscopy

In this work, we extend the theoretical framework recently developed for the simulation of resonance Raman (RR) spectra of medium-to-large sized systems to its chiral counterpart, namely, resonance Raman optical activity (RROA). The theory is based on a time-dependent (TD) formulation, with the transition tensors obtained as half-Fourier transforms of the appropriate cross-correlation functions. The implementation has been kept as general as possible, supporting adiabatic and vertical models for the PES representation, both in Cartesian and internal coordinates, with the possible inclusion of Herzberg-Teller (HT) effects. Thanks to the integration of this TD-RROA procedure within a general-purpose quantum-chemistry program, both solvation and leading anharmonicity effects can be included in an effective way. The implementation is validated on one of the smallest chiral molecule (methyloxirane). Practical applications are illustrated with three medium-size organic molecules (naproxen-OCD₃, quinidine and 2-Br-hexahelicene), whose simulated spectra are compared to the corresponding experimental data.

Computation of the S1 ← S0 Vibronic Absorption Spectrum of Formaldehyde by Variational Gaussian Wavepacket and Semiclassical IVR Methods

The vibronic absorption spectrum of the electric dipole forbidden and vibronically allowed S₁(¹ A₂) ← S₀(¹ A₁) transition of formaldehyde is calculated by Gaussian wavepacket and semiclassical methods, along with numerically exact reference calculations, using the potential energy surface of Fu, Shepler, and Bowman ( J. Am. Chem. Soc. 2011, 133, 7957). Specifically, the variational multiconfigurational Gaussian (vMCG) approach and the Herman-Kluk semiclassical initial value representation (HK-SCIVR) are compared to assess the accuracy and convergence of these methods, benchmarked against numerically exact time-dependent wavepacket propagation (TDWP) on the reference potential energy surface. The vMCG calculation is shown to converge quite well with about 100 variationally evolving Gaussian functions and using a local cubic expansion instead of the conventional local harmonic approximation. By contrast, the HK-SCIVR approach with ∼10⁵ trajectories reproduces the vibrationally structured spectral envelope correctly but yields a strongly broadened spectrum. The comparison of the computed absorption spectrum with experiment shows that the relevant vibronic progressions are reasonably reproduced by all computations, but deviations of the order of 10-100 cm^-1 occur, underscoring that both electronic structure calculations and dynamical approaches remain challenging in the calculation of typical small-molecule excited-state spectra by trajectory-based methods.

Electronic Absorption Spectra from MM and ab initio QM/MM Molecular Dynamics: Environmental Effects on the Absorption Spectrum of Photoactive Yellow Protein

We describe a new interface of the GPU parallelized TeraChem electronic structure package and the Amber molecular dynamics package for quantum mechanical (QM) and mixed QM and molecular mechanical (MM) molecular dynamics simulations. This QM/MM interface is used for computation of the absorption spectra of the photoactive yellow protein (PYP) chromophore in vacuum, aqueous solution, and protein environments. The computed excitation energies of PYP require a very large QM region (hundreds of atoms) covalently bonded to the chromophore in order to achieve agreement with calculations that treat the entire protein quantum mechanically. We also show that 40 or more surrounding water molecules must be included in the QM region in order to obtain converged excitation energies of the solvated PYP chromophore. These results indicate that large QM regions (with hundreds of atoms) are a necessity in QM/MM calculations.

Isomerization Through Conical Intersections

The standard model for photoinduced cis-trans isomerization about carbon double bonds is framed in terms of two electronic states and a one-dimensional reaction coordinate. We review recent work that suggests that a minimal picture of the reaction mechanism requires the consideration of at least two molecular coordinates and three electronic states. In this chapter, we emphasize the role of conical intersections and charge transfer in the photoisomerization mechanism.

The ground state tunneling splitting and the zero point energy of malonaldehyde: A quantum Monte Carlo determination

Quantum dynamics calculations of the ground state tunneling splitting and of the zero point energy of malonaldehyde on the full dimensional potential energy surface proposed by Yagi et al. [J. Chem. Phys. 1154, 10647 (2001)] are reported. The exact diffusion Monte Carlo and the projection operator imaginary time spectral evolution methods are used to compute accurate benchmark results for this 21-dimensional ab initio potential energy surface. A tunneling splitting of 25.7+/-0.3 cm-1 is obtained, and the vibrational ground state energy is found to be 15 122+/-4 cm-1. Isotopic substitution of the tunneling hydrogen modifies the tunneling splitting down to 3.21+/-0.09 cm-1 and the vibrational ground state energy to 14 385+/-2 cm-1. The computed tunneling splittings are slightly higher than the experimental values as expected from the potential energy surface which slightly underestimates the barrier height, and they are slightly lower than the results from the instanton theory obtained using the same potential energy surface.

The vibrational progressions of the N→V electronic transition of ethylene: A test case for the computation of Franck-Condon factors of highly flexible photoexcited molecules

The vibrational progressions of the N-->V electronic transition of ethylene--a test case for the computation of Franck-Condon factors between electronic states exhibiting very different equilibrium geometries--have been calculated by using both the Cartesian and the curvilinear internal coordinate representations of the normal modes of vibration. The comparison of the theoretical spectra with the experimental one shows that the Cartesian representation yields vibrational progressions which are not observed in the experimental spectrum, whereas the curvilinear one gives a very satisfying agreement, even in harmonic approximation.

Vibrationally mediated photodissociation of ethene isotopic variants preexcited to the fourth C–H stretch overtone

H and D photofragments produced via vibrationally mediated photodissociation of jet-cooled normal ethene (C2H4), 1,2-trans-d2-ethene (HDCCDH), and 1,1-d2-ethene (CH2CD2), initially excited to the fourth C-H stretch overtone region, were studied for the first time. H and D vibrational action spectra and Doppler profiles were measured. The action spectra include partially resolved features due to rotational cooling, while the monitored room temperature photoacoustic spectra exhibit only a very broad feature in each species. Simulation of the spectral contours allowed determination of the band types and origins, limited precision rotational constants, and linewidths, providing time scales for energy redistribution. The H and D Doppler profiles correspond to low average translational energies and show slight preferential C-H over C-D bond cleavage in the deuterated variants. The propensities toward H photofragments emerge even though the energy flow out of the initially prepared C-H stretch is on a picosecond time scale and the photodissociation occurs following internal conversion, indicating a more effective release of the light H atoms.

Nonadiabatic effects in the photoelectron spectrum of the pyrazolide-d3 anion: Three-state interactions in the pyrazolyl-d3 radical

The 351.1 nm photoelectron spectrum of the 1-pyrazolide-d(3) anion has been measured. The photoelectron angular distributions indicate the presence of nearly degenerate electronic states of the 1-pyrazolyl-d(3) radical. Equation-of-motion ionization potential coupled-cluster singles and doubles (EOMIP-CCSD) calculations have been performed to study the low-lying electronic states. The calculations strongly suggest that three electronic states, energetically close to each other, are accessed in the photodetachment process. Strong interactions of the pseudo-Jahn-Teller type in each pair of the three states are evident in the calculations for the radical at the anion geometry. Model diabatic potentials of the three states have been constructed around the anion geometry in terms of the anion reduced normal coordinates up to the second order. An analytic method to parametrize the quadratic vibronic coupling (QVC) model potentials has been introduced. Parameters of the QVC model potentials have been determined from the EOMIP-CCSD and CCSD(T) calculations. Simulations of the 1-pyrazolide-d(3) spectrum have been performed with the model Hamiltonian, treating all vibronic interactions amongst the three states simultaneously. The simulation reproduces the fine structure of the observed spectrum very well, revealing complicated nonadiabatic effects in the low-lying states of the radical. The ground state of the 1-pyrazolyl-d(3) radical is (2)A(2) and the electron affinity is 2.935+/-0.006 eV. The first excited state is (2)B(1) with a term energy of 32+/-1 meV. While the high-symmetry (C(2v)) stationary points of the X (2)A(2) and A (2)B(1) states are minima, that of the state is a saddle point as a result of the pseudo-Jahn-Teller interactions with the other two states. The topology of the adiabatic potential energy surfaces is discussed.

Photochemistry of ethylene: a multireference configuration interaction investigation of the excited-state energy surfaces

Multireference configuration interaction with singles and doubles (MR-CISD) calculations have been performed for the optimization of conical intersections and stationary points on the ethylene excited-state energy surfaces using recently developed methods for the computation of analytic gradients and nonadiabatic coupling terms. Basis set dependence and the effect of various choices of reference spaces for the MR-CISD calculations have been investigated. The crossing seam between the S0 and S1 states has been explored in detail. This seam connects all conical intersections presently known for ethylene. Major emphasis has been laid on the hydrogen-migration path. Starting in the V state of twisted-orthogonal ethylene, a barrierless path to ethylidene was found. The feasibility of ethylidene formation will be important for the explanation of the relative yield of cis and trans H2 elimination.

The photodynamics of ethylene: A surface-hopping study on structural aspects

Simulations of the photodynamics of ethylene were carried out by employing the semiempirical direct trajectory with surface hopping method in order to assess quantitatively the importance of different regions of the S(2)S(1) and S(1)S(0) crossing seams. The results show that during the first 50 fs after a vertical photoexcitation to the pipi(*) state, the nonadiabatic coupling between the S(1) and the S(2) states produces a recurrence pattern of oscillation of the populations in these states. Within the first 100 fs, the S(1) state population spans a limited region of the configuration space between the initial geometries and the twisted-pyramidalized minimum on the crossing seam (MXS). Depending on the way of counting, about 50% of the S(1)-->S(0) transitions occur in the pyramidalized region of the crossing seam, but not necessarily close to the MXS. The remaining 50% occurs in the H-migration and ethylidene regions. Our analysis shows that the ethylidene region becomes more important in later stages of the dynamics when the flux of trajectories that was not effectively converted to the ground state in the pyramidalized region starts to reach this part of the configuration space. The excited-state nonadiabatic dynamics could be employed to generate suitable initial phase space distributions for the hot-ethylene ground-state kinetic studies.

First principles simulation of the UV absorption spectrum of ethylene using the vertical Franck-Condon approach

A new method which we refer to as vertical Franck-Condon is proposed to calculate electronic absorption spectra of polyatomic molecules. In accord with the short-time picture of spectroscopy, the excited-state potential energy surface is expanded at the ground-state equilibrium geometry and the focus of the approach is more on the overall shape of the spectrum and the positions of the band maxima, rather than the precise position of the 0-0 lines. The Born-Oppenheimer approximation and the separability of the excited-state potential energy surface along the excited-state normal mode coordinates are assumed. However, the potential surface is not necessarily approximated as harmonic oscillator potentials along the individual normal modes. Instead, depending upon the nature of the potential surface along a particular normal mode, it is treated either in the harmonic approximation or the full one-dimensional potential is considered along this mode. The vertical Franck-Condon approach is applicable therefore even in cases where the excited state potential energy surface is highly anharmonic and the conventional harmonic Franck-Condon approach is inadequate. As an application of the method, the ultraviolet spectrum of ethylene between 6.2 eV (50,000 cm(-1)) and 8.7 eV (70,000 cm(-1)) is simulated, using the Similarity Transformed Equation of Motion Coupled-Cluster method to describe the required features of the potential energy surfaces. The spectrum is shown to be a result of sharp doublet structures stemming from the pi --> 3s (Rydberg) state superimposed on top of a broad band resulting from the pi --> pi* (valence) state. For the Rydberg state, the symmetric C=C stretch and the torsion mode contribute to the spectrum, while the broad valence band results from excitation into the C=C stretch, CH2 scissors, and the torsion mode. For both states, the potential along the torsion mode is highly anharmonic and the full treatment of the potential along this mode in the vertical Franck-Condon method is required.

Photoinduced dynamics of ethene in the N, V, and Z valence states: A six-dimensional nonadiabatic quantum dynamics investigation

The photoinduced dynamics of ethene following pi-->pi(*) excitation is investigated by quantum wave-packet dynamics on three coupled six-dimensional diabatic potential-energy surfaces representing the N, V, and Z valence states, which have been developed previously. The C-C stretching and torsion, as well as the pyramidalization and scissoring of both CH(2) groups are included in this description. The wave-packet calculations have been performed using the multiconfigurational time-dependent Hartree method for a time period up to 100 fs. While a small amount of population transfer to the electronic ground state is found within this period, the overall population decay time of the V state is found to exceed the 100 fs range significantly. The autocorrelation function of the wave packet and the stationary absorption spectrum of the V state also have been calculated. It is found that both the torsional mode as well as the C-C stretching mode contribute to the very extended vibrational structure of the absorption spectrum, and that both modes are strongly coupled. At least on the present ab initio surface of limited dimensionality, the speed of pyramidalization of 90 degrees twisted ethene appears as the bottleneck for the ultrafast radiationless decay of the V state.

Analysis of the mode-specific excited-state energy distribution and wavelength-dependent photoreaction quantum yield in rhodopsin

The photoreaction quantum yield of rhodopsin is wavelength dependent: phi(lambda) is reduced by up to 5% at wavelengths to the red of 500 nm but is invariant (phi = 0.65 +/- 0.01) between 450 and 500 nm (Kim et al., 2001). To understand this nonstatistical internal conversion process, these results are compared with predictions of a Landau-Zener model for dynamic curve crossing. The initial distribution of excess photon energy in the 28 Franck-Condon active vibrational modes of rhodopsin is defined by a fully thermalized sum-over-states vibronic calculation. This calculation reveals that absorption by high-frequency unreactive modes (e.g., C[double bond]C stretches) increases as the excitation wavelength is shifted from 570 to 450 nm whereas relatively less energy is deposited into reactive low-frequency modes. This result qualitatively explains the experimentally observed wavelength dependence of phi(lambda) for rhodopsin and reveals the importance of delocalized, torsional modes in the reactive pathway.