Nonvariational time-dependent multiconfiguration self-consistent field equations for electronic dynamics in laser-driven molecules

A time-dependent multiconfiguration self-consistent field (TDMCSCF) scheme is developed to describe the time-resolved electron dynamics of a laser-driven many-electron atomic or molecular system, starting directly from the time-dependent Schrodinger equation for the system. This nonvariational formulation aims at the full exploitations of concepts, tools, and facilities of existing, well-developed quantum chemical MCSCF codes. The theory uses, in particular, a unitary representation of time-dependent configuration mixings and orbital transformations. Within a short-time, or adiabatic approximation, the TDMCSCF scheme amounts to a second-order split-operator algorithm involving generically the two noncommuting one-electron and two-electron parts of the time-dependent electronic Hamiltonian. We implement the scheme to calculate the laser-induced dynamics of the two-electron H2 molecule described within a minimal basis, and show how electron correlation is affected by the interaction of the molecule with a strong laser field.     

Regarding the validity of the time-dependent Kohn-Sham approach for electron-nuclear dynamics via trajectory surface hopping

The implementation of fewest-switches surface-hopping (FSSH) within time-dependent Kohn-Sham (TDKS) theory [Phys. Rev. Lett. 95, 163001 (2005)] has allowed us to study successfully excited state dynamics involving many electronic states in a variety of molecular and nanoscale systems, including chromophore-semiconductor interfaces, semiconductor and metallic quantum dots, carbon nanotubes and graphene nanoribbons, etc. At the same time, a concern has been raised that the KS orbital basis used in the calculation provides only approximate potential energy surfaces [J. Chem. Phys. 125, 014110 (2006)]. While this approximation does exist in our method, we show here that FSSH-TDKS is a viable option for computationally efficient calculations in large systems with straightforward excited state dynamics. We demonstrate that the potential energy surfaces and nonadiabatic transition probabilities obtained within the TDKS and linear response (LR) time-dependent density functional theories (TDDFT) agree semiquantitatively for three different systems, including an organic chromophore ligating a transition metal, a quantum dot, and a small molecule. Further, in the latter case the FSSH-TDKS procedure generates results that are in line with FSSH implemented within LR-TDDFT. The FSSH-TDKS approach is successful for several reasons. First, single-particle KS excitations often give a good representation of LR excitations. In this regard, DFT compares favorably with the Hartree-Fock theory, for which LR excitations are typically combinations of multiple single-particle excitations. Second, the majority of the FSSH-TDKS applications have been performed with large systems involving simple excitations types. Excitation of a single electron in such systems creates a relatively small perturbation to the total electron density summed over all electrons, and it has a small effect on the nuclear dynamics compared, for instance, with thermal nuclear fluctuations. In such cases an additional, classical-path approximation can be made. Third, typical observables measured in time-resolved experiments involve averaging over many initial conditions. Such averaging tends to cancel out random errors that may be encountered in individual simulated trajectories. Finally, if the flow of energy between electronic and nuclear subsystems is insignificant, the ad hoc FSSH procedure is not required, and a straightforward mean-field, Ehrenfest approach is sufficient. Then, the KS representation provides rigorously a convenient and efficient basis for numerically solving the TDDFT equations of motion.     

Relaxation and dephasing in open quantum systems time-dependent density functional theory: Properties of exact functionals from an exactly-solvable model system

The dissipative dynamics of many-electron systems interacting with a thermal environment has remained a long-standing challenge within time-dependent density functional theory (TDDFT). Recently, the formal foundations of open quantum systems time-dependent density functional theory (OQS-TDDFT) within the master equation approach were established. It was proven that the exact time-dependent density of a many-electron open quantum system evolving under a master equation can be reproduced with a closed (unitarily evolving) and non-interacting Kohn-Sham system. This potentially offers a great advantage over previous approaches to OQS-TDDFT, since with suitable functionals one could obtain the dissipative open-systems dynamics by simply propagating a set of Kohn-Sham orbitals as in usual TDDFT. However, the properties and exact conditions of such open-systems functionals are largely unknown. In the present article, we examine a simple and exactly-solvable model open quantum system: one electron in a harmonic well evolving under the Lindblad master equation. We examine two different representitive limits of the Lindblad equation (relaxation and pure dephasing) and are able to deduce a number of properties of the exact OQS-TDDFT functional. Challenges associated with developing approximate functionals for many-electron open quantum systems are also discussed.     

Limits of the creation of electronic wave packets using time-dependent density functional theory

Explicitly time-dependent density functional theory (TDDFT) has often been suggested as the method of choice for controlling the correlated dynamics of many electron systems. However, it is not yet clear which control tasks can be achieved reliably and how this depends on the functionals used. In this article, we show that the control task of creating a simple wave packet, having a population of 50% in the excited state, can indeed be achieved if a certain condition is fulfilled. This result is in contrast to the observation that a full population inversion is extremely difficult to achieve. In addition, we identify a rule to predict when TDDFT produces the correct wave packet. To illustrate our findings, we study the molecules Li(2)C(2), Li(7)OH, and B(2)N(2)CO using two different functionals as well as time-dependent Hartree-Fock (TDHF). To assess the performance of TDDFT and TDHF, we compare with time-dependent configuration interaction calculations.     

Explicitly time-dependent coupled cluster singles doubles calculations of laser-driven many-electron dynamics

We report explicitly time-dependent coupled cluster singles doubles (TD-CCSD) calculations, which simulate the laser-driven correlated many-electron dynamics in molecular systems. Small molecules, i.e., HF, H(2)O, NH(3), and CH(4), are treated mostly with polarized valence double zeta basis sets. We determine the coupled cluster ground states by imaginary time propagation for these molecules. Excited state energies are obtained from the Fourier transform of the time-dependent dipole moment after an ultrashort, broadband laser excitation. The time-dependent expectation values are calculated from the complex cluster amplitudes using the corresponding configuration interaction singles doubles wave functions. Also resonant laser excitations of these excited states are simulated, in order to explore the limits for the numerical stability of our current TD-CCSD implementation, which uses time-independent molecular orbitals to form excited configurations.     

Description of molecular dynamics in intense laser fields by the time-dependent adiabatic state approach: application to simultaneous two-bond dissociation of CO2 and its control

We theoretically investigated the dynamics of structural deformations of CO(2) and its cations in near-infrared intense laser fields (approximately 10(15) W cm(-2)) by using the time-dependent adiabatic state approach. To obtain "field-following" adiabatic potentials for nuclear dynamics, the electronic Hamiltonian including the interaction with the instantaneous laser electric field is diagonalized by the multiconfiguration self-consistent-field molecular orbital method. In the CO(2) and CO(2+) stages, ionization occurs before the field intensity becomes high enough to deform the molecule. In the CO(2)(2+) stage, simultaneous symmetric two-bond stretching occurs as well as one-bond stretching. Two-bond stretching is induced by an intense field in the lowest time-dependent adiabatic state |1> of CO(2)(2+), and this two-bond stretching is followed by the occurrence of a large-amplitude bending motion mainly in the second-lowest adiabatic state |2> nonadiabatically created at large internuclear distances by the field from |1>. It is concluded that the experimentally observed stretched and bent structure of CO(2)(3+) just before Coulomb explosions originates from the structural deformation of CO(2)(2+). We also show in this report that the concept of "optical-cycle-averaged potential" is useful for designing schemes to control molecular (reaction) dynamics, such as dissociation dynamics of CO(2), in intense fields. The present approach is simple but has wide applicability for analysis and prediction of electronic and nuclear dynamics of polyatomic molecules in intense laser fields.     

Generator coordinate method in time-dependent density-functional theory: memory made simple

The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary Hamiltonians containing a deformation parameter. This paper presents a time-dependent extension of the GC method as a new approach to improve existing approximations of the exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT). The time-dependent GC method is shown to be a conceptually and computationally simple tool to build memory effects into any existing adiabatic XC potential. As an illustration, the method is applied to driven parametric oscillations of two interacting electrons in a harmonic potential (Hooke's atom). It is demonstrated that a proper choice of time-dependent generator coordinates in conjunction with the adiabatic local-density approximation reproduces the exact linear and nonlinear two-electron dynamics quite accurately, including features associated with double excitations that cannot be captured by TDDFT in the adiabatic approximation.     

Nonadiabatic coupling vectors for excited states within time-dependent density functional theory in the Tamm-Dancoff approximation and beyond

Recently, we have proposed a scheme for the calculation of nonadiabatic couplings and nonadiabatic coupling vectors within linear response time-dependent density functional theory using a set of auxiliary many-electron wavefunctions [I. Tavernelli, E. Tapavicza, and U. Rothlisberger, J. Chem. Phys. 130, 124107 (2009)]. As demonstrated in a later work [I. Tavernelli, B. F. E. Curchod, and U. Rothlisberger, J. Chem. Phys. 131, 196101 (2009)], this approach is rigorous in the case of the calculation of nonadiabatic couplings between the ground state and any excited state. In this work, we extend this formalism to the case of coupling between pairs of singly excited states with the same spin multiplicity. After proving the correctness of our formalism using the electronic oscillator approach by Mukamel and co-workers [S. Tretiak and S. Mukamel, Chem. Rev. (Washington, D.C.) 102, 3171 (2002)], we tested the method on a model system, namely, protonated formaldimine, for which we computed S(1)/S(2) nonadiabatic coupling vectors and compared them with results from high level (MR-CISD) electronic structure calculations.     

A discrete time-dependent method for metastable atoms and molecules in intense fields

The full-dimensional time-dependent Schr?dinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange mesh methods. The method is applied to calculate the quasienergies and ionization probabilities of atomic and molecular systems in intense static and dynamic electric fields. The gauge invariance and accuracy of the method is established. Applications to multiphoton ionization of positronium, the hydrogen atom and the hydrogen molecular ion are presented. At very high laser intensity, above the saturation threshold, we extend the method using a scaling technique to estimate the quasienergies of metastable states of the hydrogen molecular ion. The results are in good agreement with recent experiments.     

Excited state geometries within time-dependent and restricted open-shell density functional theories

Singlet excited state geometries of a set of medium sized molecules with different characteristic lowest excitations are studied. Geometry optimizations of excited states are performed with two closely related restricted open-shell Kohn–Sham methods and within linear response to time-dependent density functional theory. The results are compared to wave-function based methods. Excitation energies (vertical and adiabatic) calculated from the open-shell methods show systematic errors depending on the type of excitation. However, for all states accessible by the restricted methods a good agreement for the geometries with time-dependent density functional theory and wave-function based methods is found. An analysis of the energy with respect to the mixing angle for the singly occupied orbitals reveals that some states (mostly [n→π^*]) are stable when symmetry constraints are relaxed and others (mostly [π→π^*]) are instable. This has major implications on the applicability of the restricted open-shell methods in molecular dynamics simulations.     

Excitation energies,oscillator strengths,and frequency dependent polarizabilities of Be: Comparison of TDHF,EOM (second order), and MCTDHF

Low-lying excitation energies from the ground state of Be were calculated using a basis set of 61 Cartesian Gaussian functions. Three approximations were employed: the time-dependent Hartree–Fock (TDHF ), second-order equations-of-motion (EOM ), and multiconfigurational time-dependent Hartree–Fock (MCTDHF ). The TDHF excitation energies are 0.5–1.1 eV lower than experiment, and the EOM values are 0.3–1.2 eV lower than experiment, whereas the MCTDHF excitation energies deviate on the absolute average from experiment by only 0.03 eV. We found that in an MCTDHF calculation, any proper MCSCF stationary point is a good reference (i.e., initial) state, not just the ground state. Experimental values for oscillator strength are accurately known only for the 2s²X¹S → 2s2p¹P⁰ transition. The TDHF value and the MCTDHF value agree with experiment, but the EOM value does not. The agreement of the TDHF value with experiment seems to be coincidental, because for higher lying transitions the TDHF values differ by approximately a factor of two or more from the more accurate MCTDHF . Frequency independent polarizabilities, α(0), were also calculated with the TDHF , HRPA , and MCTDHF and frequency dependent polarizabilities, β(ω), were calculated with the MCTDHF . No experimental data for Be polarizabilities exist, but we expect the MCTDHF values to be among the most accurate calculations available.     

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

In this paper, we present a short account of some recent developments of self-interaction-free density-functional theory (DFT) and time-dependent density-functional theory (TDDFT) for accurate and efficient treatment of the electronic structure, and time-dependent quantum dynamics of many-electron atomic and molecular systems. The conventional DFT calculations using approximate and explicit exchange-correlation energy functional contain spurious self-interaction energy and improper long-range asymptotic potential, preventing reliable treatment of the excited, resonance, and continuum states. We survey some recent developments of DFT/TDDFT with optimized effective potential (OEP) and self-interaction correction (SIC) for both atomic and molecular systems for overcoming some of the above mentioned difficulties. These DFT (TDDFT)/OEP-SIC approaches allow the use of orbital-independent single-particle local potential which is self-interaction free. In addition we discuss several numerical techniques recently developed for efficient and high-precision treatment of the self-interaction-free DFT/TDDFT equations. The usefulness of these procedures is illustrated by a few case studies of atomic, molecular, and condensed matter processes of current interests, including (a) autoionizing resonances, (b) relativistic OEP-SIC treatment of atomic structure (Z=2-106), (c) shell-filling electronic structure in quantum dots, (d) atomic and molecular processes in intense laser fields, including multiphoton ionization, and very-high-order harmonic generation, etc. For the time-dependent processes, an alternative Floquet formulation of TDDFT is introduced for time-independent treatment of multiphoton processes in intense periodic or quasiperiodic fields. We conclude this paper with some open questions and perspectives of TDDFT.     

Development of a general time-dependent absorbing potential for the constrained adiabatic trajectory method

The constrained adiabatic trajectory method (CATM) allows us to compute solutions of the time-dependent Schro?dinger equation using the Floquet formalism and Fourier decomposition, using matrix manipulation within a non-orthogonal basis set, provided that suitable constraints can be applied to the initial conditions for the Floquet eigenstate. A general form is derived for the inherent absorbing potential, which can reproduce any dispersed boundary conditions. This new artificial potential acting over an additional time interval transforms any wavefunction into a desired state, with an error involving exponentially decreasing factors. Thus, a CATM propagation can be separated into several steps to limit the size of the required Fourier basis. This approach is illustrated by some calculations for the H(2)(+) molecular ion illuminated by a laser pulse.     

A time-dependent wave packet study of the vibronic and spin-orbit interactions in the dynamics of Cl((2)P)+H(2)-->HCl(X (1)Sigma(g) (+))+H((2)S) reaction

We investigate the vibronic and spin-orbit (SO) coupling effects in the state-selected dynamics of the title reaction with the aid of a time-dependent wave packet approach. The ab initio potential energy surfaces of Capecchi and Werner [Science 296, 715 (2002)] have been employed for this purpose. Collinear approach of the Cl((2)P) atom to the H(2) molecule splits the degeneracy of the (2)P state and gives rise to (2)Sigma and (2)Pi electronic states. These two surfaces form a conical intersection at this geometry. These states transform as 1 (2)A('), 1 (2)A("), and 2 (2)A('), respectively, at the nonlinear configurations of the nuclei. In addition, the SO interaction due to Cl atom further splits these states into (2)Sigma(1/2), (2)Pi(3/2), and (2)Pi(1/2) components at the linear geometry. The ground-state reagent Cl((2)P(3/2))+H(2) correlates with (2)Sigma(1/2) and (2)Pi(3/2), where as the SO excited reagent Cl(*)((2)P(1/2))+H(2) correlates with (2)Pi(1/2) at the linear geometry. In order to elucidate the impact of the vibronic and SO coupling effects on the initial state-selected reactivity of these electronic states we carry out quantum scattering calculations based on a flux operator formalism and a time-dependent wave packet approach. In this work, total reaction probabilities and the time dependence of electronic population of the system by initiating the reaction on each of the above electronic states are presented. The role of conical intersection alone on the reaction dynamics is investigated with a coupled two-state model and for the total angular momentum J=0 (neglecting the electronic orbital angular momentum) both in a diabatic as well as in the adiabatic electronic representation. The SO interaction is then included and the dynamics is studied with a coupled three-state model comprising six diabatic surfaces for the total angular momentum J=0.5 neglecting the Coriolis Coupling terms of the Hamiltonian. Companion calculations are carried out for the uncoupled adiabatic and diabatic surfaces in order to explicitly reveal the impact of two different surface coupling mechanisms in the dynamics of this prototypical reaction.     

Electronic excitation spectra from time-dependent density functional response theory using plane-wave methods

The time-dependent density functional response theory method for the computation of electronic excitation spectra has been implemented in a plane-wave basis set/pseudo-potential formalism. We compare our test results for N₂ and H₂CO to literature atomic basis set calculations and find good agreement. We also discuss some of the technical complications specific to the use of plane-wave basis sets. As an application, the thermally broadened photoabsorption spectrum of formamide at room temperature is computed by averaging over a number of vibrational configurations sampled from an ab initio molecular dynamics run and compared to experiment.     

New approximations for calculating dispersion coefficients

Improved approaches for finding approximate values of dispersion coefficients are proposed. They are based on scaling the values of time-dependent Hartree-Fock (TDHF) dispersion coefficients by factors that use the ratio of the estimated true value and the TDHF value of static dipole polarizabilities. It is shown that for a set of 14 atoms and molecules the average absolute-value deviation of the estimated two-body isotropic dispersion coefficients with respect to the dipole oscillator strength distribution results is smaller than 1.0% for two of our approaches. For three-body isotropic dispersion coefficients the corresponding deviations are smaller than 1.2%. Our approximations work particularly well compared to approximations proposed by other researchers in cases where the TDHF results differ from the reference values by more than 10%.     

Time-dependent configuration-interaction calculations of laser-pulse-driven many-electron dynamics: controlled dipole switching in lithium cyanide

We report simulations of laser-driven many-electron dynamics by means of the time-dependent configuration interaction singles (doubles) approach. The method accounts for the correlation of ground and excited states, is capable of describing explicitly time-dependent, nonlinear phenomena, and is systematically improvable. Lithium cyanide serves as a molecular test system in which the charge distribution and hence the dipole moment are shown to be switchable, in a controlled fashion, by (a series of) laser pulses which induce selective, state-to-state electronic transitions. One focus of our time-dependent calculations is the question of how fast the transition from the ionic ground state to a specific excited state that is embedded in a multitude of other states can be made, without creating an electronic wave packet.     

Origin of electronic structure and time-dependent state averaging in the multi-configuration time-dependent Hartree–Fock approach to electron dynamics

In this Letter, we discuss problems that can arise in the interpretation of results obtained by quantum dynamical simulations with the multi-configuration time-dependent Hartree–Fock (MCTDHF) method. In particular, we show that an effect, which can be seen as the time-dependent version of the state averaging known from standard quantum chemistry, can modify the electronic structure as derived from such a simulation. We illustrate our findings with numerical calculations for the laser excitation of a water molecule, with a Gaussian Type Orbital basis set.