Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions

An ab initio electronic wave-packet dynamics coupled with the simultaneous classical dynamics of nuclear motions in a molecule is studied. We first survey the dynamical equations of motion for the individual components. Reflecting the nonadiabatic dynamics that electrons can respond to nuclear motions only with a finite speed, the equations of motion for nuclei include a force arising from the kinematic (nuclear momentum) coupling from electron cloud. To materialize these quantum effects in the actual ab initio calculations, we study practical implementation of relevant electronic matrix elements that are related to the derivatives with respect to the nuclear coordinates. Applications of the present scheme are performed in terms of the configuration state functions (CSF) using the canonical molecular orbitals as basis functions without transformation to particular diabatic basis. In the CSF representation, the nonadiabatic interaction due to the kinematic coupling is anticipated to be rather small, and instead it should be well taken into account through the off-diagonal elements of the electronic Hamiltonian matrix. Therefore it is expected that the nonadiabatic dynamics based on this CSF basis neglecting the kinematic coupling may work. To verify this anticipation and to quantify the actual effects of the kinematic coupling, we compare the dynamics with and without the kinematic-coupling terms using the same CSF set. Applications up to the fifth electronically excited states in a nonadiabatic collision between H(2) and B(+) shows that the overall behaviors of these two calculations are surprisingly similar to each other in an average sense except for a fast fluctuation reflecting the electronic time scale. However, at the same time, qualitative differences in the collision events are sometimes observed. Therefore it turns out after all that the kinematic-coupling terms cannot be neglected in the CSF-basis representation. The present applications also demonstrate that the nonadiabatic electronic wave-packet dynamics within ab initio quantum chemical calculation is feasible.     

The electronic structure evolution of DNA during its conformation transition process

We combined classical molecular dynamics (MD) simulation with ab initio calculations to study the electronic structure evolution of DNA during its conformation transition process. By using MD simulation, we obtained the conformation transition trajectory of an oligonucleotide poly(dC)-poly(dG), from which we selected a series of representative conformations and then performed ab initio calculations for these conformations to reveal their electronic structures. Counterintuitively, the results indicate that during the conformation transition process of DNA, thermal fluctuation plays a more important role than global conformation parameters in affecting the electronic structure of DNA.     

Efficient first-principles electronic dynamics

An efficient first-principles electronic dynamics method is introduced in this article. The approach we put forth relies on incrementally constructing a time-dependent Fock∕Kohn-Sham matrix using active space density screening method that reduces the cost of computing two-electron repulsion integrals. An adaptive stepsize control algorithm is developed to optimize the efficiency of the electronic dynamics while maintaining good energy conservation. A selected set of model dipolar push-pull chromophore molecules are tested and compared with the conventional method of direct formation of the Fock∕Kohn-Sham matrix. While both methods considered herein take on identical dynamical simulation pathways for the molecules tested, the active space density screening algorithm becomes much more computationally efficient. The adaptive stepsize control algorithm, when used in conjunction with the dynamically active space method, yields a factor of ～3 speed-up in computational cost as observed in electronic dynamics using the time dependent density functional theory. The total computational cost scales nearly linear with increasing size of the molecular system.     

Excited and ground state vibrational dynamics revealed by two-dimensional electronic spectroscopy

Broadband two-dimensional electronic spectroscopy (2DES) can assist in understanding complex electronic and vibrational signatures. In this paper, we use 2DES to examine the electronic structure and dynamics of a long chain cyanine dye (1,1-diethyl-4,4-dicarbocyanine iodide, or DDCI-4), a system with a vibrational progression. Using broadband pulses that span the resonant electronic transition, we measure two-dimensional spectra that show a characteristic six peak pattern from coherently excited ground and excited state vibrational modes. We model these features using a spectral density formalism and the vibronic features are assigned to Feynman pathways. We also examine the dynamics of a particular set of peaks demonstrating anticorrelated peak motion, a signature of oscillatory wavepacket dynamics on the ground and excited states. These dynamics, in concert with the general structure of vibronic two-dimensional spectra, can be used to distinguish between pure electronic and vibrational quantum coherences.     

On the gauge invariance of nonperturbative electronic dynamics using the time-dependent Hartree-Fock and time-dependent Kohn-Sham

Nonperturbative electronic dynamics using the time-dependent Hartree-Fock (TDHF) and time-dependent Kohn-Sham (TDKS) theories with the adiabatic approximation is a powerful tool in obtaining insights into the interaction between a many-electron system and an external electromagnetic field. In practical applications of TDHF/TDKS using a truncated basis set, the electronic dynamics and molecular properties become gauge-dependent. Numerical simulations are carried out in the length gauge and velocity gauge to verify the extent of gauge-dependence using incomplete basis sets. Electronic dynamics of two many-electron systems, a helium atom and a carbon monoxide molecule in high-intensity linearly polarized radiation fields are performed using the TDHF and TDKS with two selected adiabatic exchange-correlation (xc) functionals. The time evolution of the expectation values of the dipole moment and harmonic spectra are calculated in the two gauges, and the basis set dependence on the gauge-invariance of these properties is investigated.     

Geometric and electronic structure of clusters

The interplay between electronic and geometric structure is investigated for covalently bonded phosphorus clusters. We use a modification of the molecular dynamics/ density functional (MD/DF) method of Car and Parrinello, describing the electronic structure by a simplified linear combination of atomic orbitals (LCAO) approach. The results show clearly the tendency of phosphorus to threefold coordination, and substantial variations in bond angles lead to a large variety of isomers.     

Site-directed electronic tunneling through a vibrating molecular network

The effect of electronic-nuclear coupling on electronic transport through a complex molecular network is studied. Electronic tunneling dynamics in a network of N donor/acceptor sites, connected by molecular bridges, is shown to be controlled by electronic-nuclear coupling at the bridges. Particularly, electronic coupling to an accepting nuclear mode at the contact site between the donor and the rest of the network is shown to affect the tunneling path selection to specific acceptors. In the "deep" tunneling regime, the network is mapped onto an N-level system using a recursive perturbation expansion, enabling analytical treatment of the electronic dynamics. The analytic formulation is applied for two model systems, demonstrating site-directed tunneling by electronic-nuclear coupling. Numerical simulations suggest that this phenomenon is not limited to the deep tunneling regime.     

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. II. Coulomb interaction effects in single conjugated polymer chains

Conjugated polymers have attracted considerable attention in the last few decades due to their potential for optoelectronic applications. A key step that needs optimisation is charge carrier separation following photoexcitation. To understand better the dynamics of the exciton prior to charge separation, we have performed simulations of the formation and dynamics of localised excitations in single conjugated polymer strands. We use a nonadiabatic molecular dynamics method which allows for the coupled evolution of the nuclear degrees of freedom and of multiconfigurational electronic wavefunctions. We show the relaxation of electron-hole pairs to form excitons and oppositely charged polaron pairs and discuss the modifications to the relaxation process predicted by the inclusion of the Coulomb interaction between the carriers. The issue of charge photogeneration in conjugated polymers in dilute solution is also addressed.     

Femtosecond studies of tryptophan fluorescence dynamics in proteins: local solvation and electronic quenching

We report our systematic examination of tryptophan fluorescence dynamics in proteins with femtosecond resolution. Distinct patterns of femtosecond-resolved fluorescence transients from the blue to the red side of emission have been characterized to distinguish local ultrafast solvation and electronic quenching. It is shown that tryptophan is an ideal local optical probe for hydration dynamics and protein-water interactions as well as an excellent local molecular reporter for ultrafast electron transfer in proteins, as demonstrated by a series of biological systems, here in melittin, human serum albumin, and human thioredoxin, and at lipid interfaces. These studies clarify the assignments in the literature about the ultrafast solvation or quenching dynamics of tryptophan in proteins. We also report a new observation of solvation dynamics at far red-side emission when the relaxation of the local environment is slower than 1 ps. These results provide a molecular basis for using tryptophan as a local molecular probe for ultrafast protein dynamics in general.     

A sequential molecular mechanics/quantum mechanics study of the electronic spectra of amides

We report gas-phase electronic spectra of formamide, N-methyformamide, acetamide, and N-methylacetamide at 300 K calculated using a combination of classical molecular dynamics and time-dependent density functional theory (TDDFT). In comparison to excitation energies computed using the global minima structures, the valence npi* and pi(nb)pi* states show a significant red-shift of 0.1-0.35 eV, while smaller shifts are found for the n3s and pi(nb)3s Rydberg states. In this work, we have identified the physical origin of these shifts arising from variations of the molecular structure. We present simple relationships between key geometrical parameters and spectral shifts. Consequently, electronic spectra can be generated directly from ground-state structures, without additional quantum chemical calculations. The electronic spectrum of formamide in aqueous solution is computed using TDDFT using an explicit solvent model. This provides a quantitative determination of the condensed-phase spectrum. In general, this study shows that temperature effects can change the predicted excitation energies significantly and demonstrates how electronic spectra at elevated temperatures can be computed in a computationally efficient way.     

Studies of impulsive vibrational influence on ultrafast electronic excitation transfer

We investigated electronic energy-transfer dynamics in three model dimers within which coherent intramonomer nuclear motion had been induced by impulsive Raman excitation using an optimized, electronically preresonant control pulse. Calculations of the donor-survival probability, the ultrafast pump-probe signal, and the pump-probe difference signal are presented for dithia-anthracenophane and homodimers of 2-difluoromethylanthracene and 2-trifluoromethylanthracene. Survival probabilities and signals, along with phase-space analyses, elucidated the mechanisms, extent, and spectroscopic manifestations of external vibrational or torsional control over electronic excitation transfer.     

The Jahn-Teller effect in the triply degenerate electronic state of methane radical cation

A quantum dynamics study is performed to examine the complex nuclear motion underlying the first photoelectron band of methane. The broad and highly overlapping structures of the latter are found to originate from transitions to the ground electronic state, X(2)T(2), of the methane radical cation. Ab initio calculations have also been carried out to establish the potential energy surfaces for the triply degenerate electronic manifold of CH(4)(+). A suitable diabatic vibronic Hamiltonian has been devised and the nonadiabatic effects due to Jahn-Teller conical intersections on the vibronic dynamics investigated in detail. The theoretical results show fair accord with experiment.     

Molecular and electronic structure of 1,8-peribridged naphthalenes

The crystal and molecular structure of 1,8-thianaphthalene has been determined and compared with other single-atom peribridged naphthalenes (SAPN). The measured CSC angle is 73.06 degrees, which is the smallest bridging angle yet recorded for a SAPN derivative. The ab initio calculations using G3(MP2)//B3LYP method were performed for peribridged naphthalenes in order to determine how the strain of the four-membered ring is influenced by the type of bridge linking 1,8 positions. The electronic structure of 1,8-thia- and 1,8-sulfonenaphthalenes has been studied by UV photoelectron spectroscopy. We have tried to identify and distinguish the strain effect on the electronic structure of the naphthalene moiety.     

Revisiting the electronic excited-state hydrogen bonding dynamics of coumarin chromophore in alcohols: Undoubtedly strengthened not cleaved

In the present work, the electronic excited-state hydrogen bonding dynamics of coumarin chromophore in alcohols is revisited. The time-dependent density functional theory (TDDFT) method has been performed to investigate the intermolecular hydrogen bonding between Coumarin 151 (C151) and methanol (MeOH) solvent in the electronic excited state. Three types of intermolecular hydrogen bonds can be formed in the hydrogen-bonded C151–(MeOH)₃ complex. We have demonstrated again that intermolecular hydrogen bonds between C151 and methanol molecules can be significantly strengthened upon photoexcitation to the electronically excited state of C151 chromophore. Our results are consistent with the intermolecular hydrogen bond strengthening in the electronically excited state of Coumarin 102 in alcoholic solvents, which has been demonstrated for the first time by Zhao et al. At the same time, the electronic excited-state hydrogen bond cleavage mechanism of photoexcited coumarin chromophores in alcohols proposed in some other studies about the hydrogen bonding dynamics is undoubtedly excluded. Hence, we believe that the two contrary dynamic mechanisms for intermolecular hydrogen bonding in electronically excited states of coumarin chromophores in alcohols are clarified here.     

A model electronic Hamiltonian to study low-lying electronic states of [Fe(bpy)3]2+ in aqueous solution

A simple model electronic Hamiltonian to describe the potential energy surfaces of several low-lying d-d states of the [Fe(bpy)(3)](2+) complex is developed for use in molecular dynamics (MD) simulation studies. On the basis of a method proposed previously for first-row transition metal ions in aqueous solution, the model Hamiltonian is constructed using density functional theory calculations for the lowest singlet and quintet states. MD simulations are then carried out for the two spin states in aqueous solution in order to examine the performance of the model Hamiltonian. The simulation results indicate that the present model electronic Hamiltonian reasonably describes the potential energy surfaces of the two spin states of the aqueous [Fe(bpy)(3)](2+) system, while retaining sufficient simplicity for application in simulation studies on excited state dynamics.     

Anti-correlated spectral motion in bisphthalocyanines: evidence for vibrational modulation of electronic mixing

We exploit a coherently excited nuclear wave packet to study nuclear motion modulation of electronic structure in a metal bridged phthalocyanine dimer, lutetium bisphthalocyanine, which displays two visible absorption bands. We find that the nuclear coordinate influences the energies of the underlying exciton and charge resonance states as well as their interaction; the interplay of the various couplings creates unusual anti-correlated spectral motion in the two bands. Excited state relaxation dynamics are the same regardless of which transition is pumped, with decay time constants of 1.5 and 11 ps. The dynamics are analyzed using a three-state kinetic model after relaxation from one or two additional states faster than the experimental time resolution of 50-100 fs.     

Born-Oppenheimer approximation and beyond for time-dependent electronic processes

Explicit computations of electronic motion in time and space are gradually becoming feasible and available. The knowledge of this motion is of relevance by itself but is also important for understanding available and predicting future experiments on the electronic time scale. In electronic processes of interest, usually several and even many stationary electronic states participate and the obvious question arises on how to describe the accompanying quantum nuclear dynamics at least on the time scale of the process. In this work, we attempt to study the nuclear dynamics in the framework of a fully time-dependent Born-Oppenheimer approximation. Additionally, we attempt to go beyond this approximation by introducing the coupling of several electronic wavepackets by the nuclear wavepackets. In this context, we also discuss a time-dependent transformation to diabatic electronic wavepackets. A simple but critical model of charge transfer is analyzed in some detail on various levels of approximation and also solved exactly.