Design of an infrared laser pulse to control the multiphoton dissociation of the Fe-CO bond in CO-heme compounds

Optimal control theory is used to design a laser pulse for the multiphoton dissociation of the Fe-CO bond in the CO-heme compounds. The study uses a hexacoordinated iron-porphyrin-imidazole-CO complex in its ground electronic state as a model for CO liganded to the heme group. The potential energy and dipole moment surfaces for the interaction of the CO ligand with the heme group are calculated using density functional theory. Optimal control theory, combined with a time-dependent quantum dynamical treatment of the laser-molecule interaction, is then used to design a laser pulse capable of efficiently dissociating the CO-heme complex model. The genetic algorithm method is used within the mathematical framework of optimal control theory to perform the optimization process. This method provides good control over the parameters of the laser pulse, allowing optimized pulses with simple time and frequency structures to be designed. The dependence of photodissociation yield on the choice of initial vibrational state and of initial laser field parameters is also investigated. The current work uses a reduced dimensionality model in which only the Fe-C and C-O stretching coordinates are explicitly taken into account in the time-dependent quantum dynamical calculations. The limitations arising from this are discussed in Sec. IV.     

Time-dependent density functional theoretical study of low lying excited states of F2

The utility of time-dependent density functional theory (TDDFT) in predicting excitation energies is tested for the low lying excited states of F₂, a system that has posed severe challenges to ab initio quantum theory. It is shown that TDDFT using B3LYP functional predicts the excitation energies in good agreement with experiment. In some cases, the agreement is better than that for the post-Hartree–Fock methods like CASSCF and MRCI.     

Excitation, dynamics, and control of rotationally autoionizing Rydberg states of H2

The dynamics of rotationally autoionizing Rydberg states of molecular hydrogen is investigated using a time-dependent extension of multichannel quantum defect theory, in which the time-dependent wave packets are constructed using first-order perturbation theory. An analytical expression for the complex excitation function for a sequence of Gaussian excitation pulses is derived and then employed to investigate the influence of pairs of pulses with well-defined phase differences on the decay dynamics and final-state composition.     

Resonant transfer of excitation between two molecules using Maxwell fields

The matrix element for the resonant transfer of excitation between two molecules possessing electric and magnetic multipole moments of arbitrary order is calculated using quantum electrodynamical response theory. A prerequisite of the method is the functional form for the lth order linear electric and magnetic multipole dependent electric displacement and magnetic field operators in the neighborhood of a molecule, whose derivation is also given. The initially unexcited species is viewed as a test body accepting energy resonantly via coupling to the Maxwell fields of the excited multipole source molecule. The generalized electric-electric multipole contribution to the matrix element is shown to agree with an earlier calculation using time-dependent perturbation theory. As an application involving both electric and magnetic terms, the rate of excitation transfer between two chiral molecules is computed and found to depend on the handedness of each species.     

Quantum beats and Kepler motion in fast competing photoionization and photodissociation processes

Electronic and nuclear wavepackets created by coherent excitation of an autoionized and predissociated 'complex' resonance in H2 are studied theoretically using time-dependent multichannel quantum defect theory. The calculations predict that quantum beats between the components of the complex resonance interfere with Rydberg wavepacket (Kepler) motion to yield characteristic 'mixed' flux patterns in the observable time-dependent ionization and dissociation signals.     

Quantum dynamics of the CH3 fragment: a curvilinear coordinate system and kinetic energy operators

A curvilinear coordinate system for AB(3) fragments is given. The corresponding exact kinetic energy operator is derived and a series of simpler, progressively more approximate kinetic energy operators are suggested. The operators are tailored for quantum dynamics simulations using the multiconfigurational time-dependent Hartree approach. It is outlined how these fragment coordinates can be utilized to set up coordinate systems for larger systems such as AB(3)C or AB(3)CD. Calculations of the vibrational levels of CH(3) and quantum dynamics studies investigate the accuracy of the different kinetic energy operators suggested.     

Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

A nonlinear conjugate gradient optimization scheme is used to obtain excitation energies within the random phase approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size N is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular-orbital-free algorithm is found to be robust and computationally efficient, providing a first step toward large-scale, reduced complexity calculations of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent density functional theory.     

Time-dependent four-component relativistic density functional theory for excitation energies

Time-dependent four-component relativistic density functional theory within the linear response regime is developed for calculating excitation energies of heavy element containing systems. Since spin is no longer a good quantum number in this context, we resort to time-reversal adapted Kramers basis when deriving the coupled Dirac-Kohn-Sham equation. The particular implementation of the formalism into the Beijing density functional program package utilizes the multipolar expansion of the induced density to facilitate the construction of the induced Coulomb potential. As the first application, pilot calculations on the valence excitation energies and fine structures of the rare gas (Ne to Rn) and Group 12 (Zn to Hg) atoms are reported. To the best of our knowledge, it is the first time to be able to account for spin-orbit coupling within time-dependent density functional theory for excitation energies.     

Theoretical study on the excited-state intramolecular proton transfer in the aromatic schiff base salicylidene methylamine: an electronic structure and quantum dynamical approach

The proton-transfer dynamics in the aromatic Schiff base salicylidene methylamine has been theoretically analyzed in the ground and first singlet (pi,pi) excited electronic states by density functional theory calculations and quantum wave-packet dynamics. The potential energies obtained through electronic calculations that use the time-dependent density functional theory formalism, which predict a barrierless excited-state intramolecular proton transfer, are fitted to a reduced three-dimensional potential energy surface. The time evolution in this surface is solved by means of the multiconfiguration time-dependent Hartree algorithm applied to solve the time-dependent Schr?dinger equation. It is shown that the excited-state proton transfer occurs within 11 fs for hydrogen and 25 fs for deuterium, so that a large kinetic isotope effect is predicted. These results are compared to those of the only previous theoretical work published on this system [Zgierski, M. Z.; Grabowska, A. J. Chem. Phys. 2000, 113, 7845], reporting a configuration interaction singles barrier of 1.6 kcal mol(-1) and time reactions of 30 and 115 fs for the hydrogen and deuterium transfers, respectively, evaluated with the semiclassical instanton approach.     

Time-dependent density functional theory gradients in the Amsterdam density functional package: geometry optimizations of spin-flip excitations

An implementation of time-dependent density functional theory (TDDFT) energy gradients into the Amsterdam density functional theory program package (ADF) is described. The special challenges presented by Slater-type orbitals in quantum chemical calculation are outlined with particular emphasis on details that are important for TDDFT gradients. Equations for the gradients of spin-flip TDDFT excitation energies are derived. Example calculations utilizing the new implementation are presented. The results of standard calculations agree well with previous results. It is shown that starting from a triplet reference, spin-flip TDDFT can successfully optimize the geometry of the four lowest singlet states of CH₂ and three other isovalent species. Spin-flip TDDFT is used to calculate the potential energy curve of the breaking of the C?CC bond of ethane. The curve obtained is superior to that from a restricted density functional theory calculation, while at the same time the problems with spin contamination exhibited by unrestricted density functional theory calculations are avoided.     

Laser control of vibrational excitation in carboxyhemoglobin: a quantum wave packet study

A coherent control algorithm is applied to obtain complex-shaped infrared laser pulses for the selective vibrational excitation of carbon monoxide at the active site of carbonmonoxyhemoglobin, modeled by the six-coordinated iron-porphyrin-imidazole-CO complex. The influence of the distal histidine is taken into account by an additional imidazole molecule. Density-functional theory is employed to calculate a multidimensional ground-state potential energy surface, and the vibrational dynamics as well as the laser interaction is described by quantum wave-packet calculations. At each instant in time, the optimal electric field is calculated and used for the subsequent quantum dynamics. The results presented show that the control scheme is applicable to complex systems and that it yields laser pulses with complex time-frequency structures, which, nevertheless, have a clear physical interpretation.     

Computational studies of photophysical properties of porphin, tetraphenylporphyrin and tetrabenzoporphyrin

The molecular photonics of porphyrins are studied using a combination of first-principle and semi-empirical calculations. The applicability of the approach is demonstrated by calculations on free-base porphyrin, tetraphenylporphyrin, and tetrabenzoporphyrin. The method uses excitation energies and oscillator strengths calculated at the linear-response time-dependent density functional theory (TDDFT) or the corresponding values calculated at the linear-response approximate second-order coupled-cluster (CC2) levels. The lowest singlet excitation energies obtained in the TDDFT and CC2 calculations are 0.0-0.28 eV and 0.18-0.47 eV larger than the experimental values, respectively. The excitation energies for the first triplet state calculated at the TDDFT level are in excellent agreement with experiment, whereas the corresponding CC2 values have larger deviations from experiment of 0.420.66 eV. The matrix elements of the spin-orbit and non-adiabatic coupling operators have been calculated at the semi-empirical intermediate neglect of differential overlap (INDO) level using a spectroscopic parameterization. The calculations yield rate constants for internal conversion and intersystem crossing processes as well as quantum yields for fluorescence and phosphorescence. The main mechanism for the quenching of fluorescence in tetraphenylporphyrin and tetrabenzoporphyrin is the internal conversion, whereas for free-base porphyrin both the internal conversion and the intersystem crossing processes reduce the fluorescence intensity. The phosphorescence is quenched by a fast internal conversion from the triplet to the ground state.     

Forward-backward semiclassical and quantum trajectory methods for time correlation functions

Forward-backward trajectory formulations of time correlation functions are reviewed. Combination of the forward and reverse time evolution operators within the time-dependent semiclassical approximation minimizes phase cancellation, giving rise to an efficient methodology for simulating the dynamics of low-temperature fluids. A quantum mechanical version of the forward-backward formulation, based on the hydrodynamic formulation of time-dependent quantum mechanics, is also available but is practical only for small systems.     

Excitation energy transfer (EET) between molecules in condensed matter: a novel application of the polarizable continuum model (PCM)

We present a quantum-mechanical theory to study excitation energy transfers between molecular systems in solution. The model is developed within the time-dependent (TD) density-functional theory and the solvent effects are introduced in terms of the polarizable continuum model (PCM). Unique characteristic of this model is that both "reaction field" and screening effects are included in a coherent and self-consistent way. This is obtained by introducing proper solvent-specific operators in the Kohn-Sham equations and in the corresponding TD scheme. The solvation model exploits the integral equation formalism (IEF) version of PCM and it defines the solvent operators on a molecular cavity modeled on the real three-dimensional (3D) structure of the solute systems. Applications to EET in dimers of ethylene and naphtalene are presented and discussed.     

含时密度矩阵重正化群的理论与应用

密度矩阵重正化群(DMRG)作为计算低维强关联体系强有力的方法为人熟知, 在量子化学电子结构计算中得到广泛应用. 最近几年, 含时密度矩阵重正化群(TD-DMRG)的理论取得较快发展, TD-DMRG逐渐成为复杂体系量子动力学理论模拟的重要新兴方法之一. 本文综述了基于矩阵乘积态(MPS) 和矩阵乘积算符(MPO)的DMRG基本理论, 并重点介绍了若干最常见的TD-DMRG时间演化算法, 包括基于演化再压缩(P&C) 的算法、 基于含时变分原理(TDVP)的算法和时间步瞄准(TST)算法; 还对利用TD-DMRG模拟有限温体系的纯化(Purification)算法和最小纠缠典型量子热态(METTS)算法进行了介绍. 最后, 对近年TD-DMRG在复杂体系量子动力学中的应用进行了总结.     

Coherent control of wavepacket dynamics by locally designed external field

A new coherent control theory for manipulating quantum mechanical dynamics is proposed. The control field is designed locally (in time domain) so as to realize monotonous increase of the overlap between currently evolving wavefunction and the time-dependent target state, which will eventually reach to a desired quantum state under field-free condition. The present theory is applied to one-dimensional harmonic oscillator and Morse potential systems.     

Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock

A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples.     

A dual-level state-specific time-dependent density-functional theory

A highly efficient new algorithm for time-dependent density-functional theory (TDDFT) calculations is presented. In this algorithm, a dual-level approach to speed up DFT calculations (Nakajima and Hirao, J Chem Phys 2006, 124, 184108) is combined with a state-specific (SS) algorithm for TDDFT (Chiba et al., Chem Phys Lett 2006, 420, 391). The dual-level SS-TDDFT algorithm was applied to excitation energy calculations of typical small molecules, the Q bands of the chlorophyll A molecule, the charge-transfer energy of the zincbacteriochlorin-bacteriochlorin model system, and the lowest-lying excitation of the circumcoronene molecule. As a result, it was found that the dual-level SS-TDDFT gave correct excitation energies with errors of 0.2-0.3 eV from the standard TDDFT approach, with much lower CPU times for various types of excitation energies of large-scale molecules.     

Solutions to the time-dependent,forced quantum oscillator equation in the coordinate representation

Time-dependent creation and annihilation operators are derived which are used to obtain exact solutions, in the coordinate representation, to the time-dependent, forced quantum oscillator equation. The solutions are used to obtain a general formula for the transition probabilities, valid for any time-dependent force.     

Theoretical investigation of the mechanism and dynamics of intramolecular coherent resonance energy transfer in soft molecules: a case study of dithia-anthracenophane

A computational study is conducted on dithia-anthracenophane (DTA), for which there is experimental evidence for coherent resonance energy transfer dynamics, and on dimethylanthracene (DMA), a molecule representing the energy donor and the acceptor in DTA. Electronic excitation energies are calculated by configuration interaction singles (CIS) and time-dependent density functional theory (TD-DFT) methods and are compared to experimental ones. Electronic coupling constants are calculated between two DMAs embedded into the ground-state structure of DTA employing methods based on transition densities. The resulting values of electronic coupling provide a more consistent interpretation of experiments than those based on one-half the level spacing of DTA excitation energies. Solvation effects are studied based on the polarizable continuum model (PCM). Solvent-induced polarization and screening effects are shown to make opposite contributions, and the net electronic coupling is little different from the value in a vacuum. The likelihood of coherent population transfer is assessed on the basis of a recently developed theory of coherent resonance energy transfer. The time scale of bath is shown to have an important role in sustaining the quantum coherence. The combination of quantum chemical and dynamical data suggests that the electronic coupling in DTA is in the range of 50-100 cm(-1). The presence of oscillatory excitation population dynamics can be understood from the picture of polaronic excitation moderately dressed with dispersive vibrational modes. The effect of torsional modulation on the excitation energies of DTA and electronic coupling is examined on the basis of optimized structures with the torsional angle constrained. The result suggests that inelastic effect due to torsional motion cannot be disregarded in DTA.