Linear-scaling quantum mechanical methods for excited states

The poor scaling of many existing quantum mechanical methods with respect to the system size hinders their applications to large systems. In this tutorial review, we focus on latest research on linear-scaling or O(N) quantum mechanical methods for excited states. Based on the locality of quantum mechanical systems, O(N) quantum mechanical methods for excited states are comprised of two categories, the time-domain and frequency-domain methods. The former solves the dynamics of the electronic systems in real time while the latter involves direct evaluation of electronic response in the frequency-domain. The localized density matrix (LDM) method is the first and most mature linear-scaling quantum mechanical method for excited states. It has been implemented in time- and frequency-domains. The O(N) time-domain methods also include the approach that solves the time-dependent Kohn-Sham (TDKS) equation using the non-orthogonal localized molecular orbitals (NOLMOs). Besides the frequency-domain LDM method, other O(N) frequency-domain methods have been proposed and implemented at the first-principles level. Except one-dimensional or quasi-one-dimensional systems, the O(N) frequency-domain methods are often not applicable to resonant responses because of the convergence problem. For linear response, the most efficient O(N) first-principles method is found to be the LDM method with Chebyshev expansion for time integration. For off-resonant response (including nonlinear properties) at a specific frequency, the frequency-domain methods with iterative solvers are quite efficient and thus practical. For nonlinear response, both on-resonance and off-resonance, the time-domain methods can be used, however, as the time-domain first-principles methods are quite expensive, time-domain O(N) semi-empirical methods are often the practical choice. Compared to the O(N) frequency-domain methods, the O(N) time-domain methods for excited states are much more mature and numerically stable, and have been applied widely to investigate the dynamics of complex molecular systems.     

Quantum chemical methods for the investigation of photoinitiated processes in biological systems: theory and applications.

With the advent of modern computers and advances in the development of efficient quantum chemical computer codes, the meaningful computation of large molecular systems at a quantum mechanical level became feasible. Recent experimental effort to understand photoinitiated processes in biological systems, for instance photosynthesis or vision, at a molecular level also triggered theoretical investigations in this field. In this Minireview, standard quantum chemical methods are presented that are applicable and recently used for the calculation of excited states of photoinitiated processes in biological molecular systems. These methods comprise configuration interaction singles, the complete active space self-consistent field method, and time-dependent density functional theory and its variants. Semiempirical approaches are also covered. Their basic theoretical concepts and mathematical equations are briefly outlined, and their properties and limitations are discussed. Recent successful applications of the methods to photoinitiated processes in biological systems are described and theoretical tools for the analysis of excited states are presented.     

Linear-scaling computation of excited states in time-domain

The applicability of quantum mechanical methods is severely limited by their poor scaling.To circumvent the problem,linearscaling methods for quantum mechanical calculations had been developed.The physical basis of linear-scaling methods is the locality in quantum mechanics where the properties or observables of a system are weakly influenced by factors spatially far apart.Besides the substantial efforts spent on devising linear-scaling methods for ground state,there is also a growing interest in the development of linear-scaling methods for excited states.This review gives an overview of linear-scaling approaches for excited states solved in real time-domain.     

The use of Raman spectroscopy to study photodissociation dynamics for systems where curve crossing is important

We present exact time-dependent quantum mechanical calculations of Raman intensities for a model H₃⁺ system that includes two coupled excited electronic states. The sensitivitiy of the Raman intensities on the magnitude of the coupling between the upper surfaces, and on the orientation of the transition dipoles (taken to be either parallel or antiparallel), is explored.     

Quantum chemical study of the photocoloration reaction in the napthoxazine series

Ab initio and semiempirical quantum mechanical calculations were performed to study the electronic spectra of spiroxazine photochromic compounds as well as the corresponding photoisomers. Ground-state geometries were optimized based on density functional theory (DFT). Excitation energies of the different forms were calculated using the time-dependent density functional theory (TD-DFT) method. Semiempirical calculations including configuration interactions were performed to detail the mechanism of ring opening in excited states. On the basis of the obtained potential energy profile, a complete mechanism of photocoloration able to clarify some experimental findings is provided. A correlation of the experimental quantum yield of photocoloration with the calculated properties as a function of substituent effects is proposed.     

Exploiting graphical processing units to enable quantum chemistry calculation of large solvated molecules with conductor-like polarizable continuum models

The conductor-like polarizable continuum model (C-PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in quantum chemistry. We have previously implemented C-PCM solvation for Hartree-Fock (HF) and density functional theory (DFT) on graphical processing units (GPUs), enabling the quantum mechanical treatment of large solvated biomolecules. Here, we first propose a GPU-based algorithm for the PCM conjugate gradient linear solver that greatly improves the performance for very large molecules. The overhead for PCM-related evaluations now consumes less than 15% of the total runtime for DFT calculations on large molecules. Second, we demonstrate that our algorithms tailored for ground state C-PCM are transferable to excited state properties. Using a single GPU, our method evaluates the analytic gradient of the linear response PCM time-dependent density functional theory energy up to 80× faster than a conventional central processing unit (CPU)-based implementation. In addition, our C-PCM algorithms are transferable to other methods that require electrostatic potential (ESP) evaluations. For example, we achieve speed-ups of up to 130× for restricted ESP-based atomic charge evaluations, when compared to CPU-based codes. We also summarize and compare the different PCM cavity discretization schemes used in some popular quantum chemistry packages as a reference for both users and developers.     

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.     

Structural and spectral properties of 4-bromo-1-naphthyl chalcones: a quantum chemical study

The structural and optical properties of 4-bromo-1-naphthyl chalcones (BNC) have been studied by using quantum chemical methods. The density functional theory (DFT) and the singly excited configuration interaction (CIS) methods were employed to optimize the ground and excited state geometries of unsubstituted and substituted BNC with different electron withdrawing and donating groups in both gas and solvent phases. Based on the ground and excited state geometries, the absorption and emission spectra of BNC molecules were calculated using the time-dependent density functional theory (TDDFT) method. The solvent phase calculations were performed using the polarizable continuum model (PCM). The geometrical parameters, vibrational frequencies, and relative stability of cis- and trans-isomers of unsubstituted and substituted BNC molecules have been studied. The results from the TDDFT calculations reveal that the substitution of electron withdrawing and electron donating groups affects the absorption and emission spectra of BNC.     

Analysis and prediction of absorption band shapes, fluorescence band shapes, resonance Raman intensities, and excitation profiles using the time-dependent theory of electronic spectroscopy

A general method for the simulation of absorption (ABS) and fluorescence band shapes, resonance-Raman (rR) spectra, and excitation profiles based on the time-dependent theory of Heller is discussed. The following improvements to Heller's theory have been made: (a) derivation of new recurrence relations for the time-dependent wave packet overlap in the case of frequency changes between the ground and electronically excited states, (b) a new series expansion that gives insight into the nature of Savin's preresonance approximation, (c) incorporation of inhomogeneous broadening effects into the formalism at no additional computational cost, and (d) derivation of a new and simple short-time dynamics based equation for the Stokes shift that remains valid in the case of partially resolved vibrational structure. Our implementation of the time-dependent theory for the fitting of experimental spectra and the simulation of model spectra as well as the quantum mechanical calculation of the model parameters is discussed. The implementation covers all electronic structure approaches which are able to deliver ground- and excited-state energies and transition dipole moments. The technique becomes highly efficient if analytic gradients for the excited-state surface are available. In this case, the computational cost for the simultaneous prediction of ABS, fluorescence, and rR spectra is equal to that of a single excited-state geometry optimization step while the limitations of the short-time dynamics approximation are completely avoided. As a test case we discuss the well-known case of the strongly allowed 1 (1)A(g) --> 1 (1)B(u) transition in 1,3,5 trans-hexatriene in detail using method ranging from simple single-reference treatments to elaborate multireference electronic structure approaches. At the highest computational level, the computed spectra show the best agreement that has so far been obtained with quantum chemical methods for this problem.     

Quantum mechanical investigations of the N(4S)+O2(X 3Sigmag -)-->NO(X 2Pi)+O(3P) reaction

The reaction between energetic nitrogen atoms and oxygen molecules has received important attention in connection with nitric oxide chemistry in the lower thermosphere. We report time-independent quantum mechanical calculations of the N(4S)+O2-->NO+O reaction employing the X 2A' and a 4A' electronic potential energy surfaces of Sayos et al. [J. Chem. Phys. 117, 670 (2002)]. We confirm the production of highly vibrationally excited NO molecules, consistent with previous semiclassical and more recent time-dependent quantum wave packet studies. Calculations are carried out for total angular momentum quantum number J=0 and cross sections and rate coefficients are extracted using the J-shifting approximation. The results are in good agreement with available experimental and theoretical data.     

Time-dependent quantum dynamical simulations of C2 condensation under extreme conditions

We report theoretical studies of the initial phase of bulk C(2) condensation into carbon nano-structures by means of Born-Oppenheimer and time-dependent quantum mechanical Liouville-von Neumann molecular dynamics based on the density-functional tight-binding (DFTB) framework for electrons. We observe that the time-dependent quantum mechanical approach leads to faster formation of carbon nanostructures than analogous Born-Oppenheimer simulations. Our results suggest that the condensation of bulk carbon is nonadiabatic in nature, with the critical role of electronic stopping as in ion-irradiation of materials. Contrary to time-dependent quantum mechanical simulations, Born-Oppenheimer dynamics incorrectly predict that the short carbon chains obtained from initial reactive collisions between C(2) quickly evaporate, leading to much lower probability of secondary collisions and condensation. We also discuss some deficiencies in Born-Oppenheimer dynamics that lead to unphysical charge polarization and electron transfer.     

Fluorescence spectra of organic dyes in solution: a time dependent multilevel approach

Classical all-atom molecular dynamics (MD) simulations and quantum mechanical (QM) time-dependent density functional theory (TD-DFT) calculations are employed to study the conformational and photophysical properties of the first emitter excited state of tetramethyl-rhodamine iso-thiocyanate fluorophore in aqueous solution. For this purpose, a specific and accurate force field has been parameterised from QM data to model the fluorophore's first bright excited state. During the MD simulations, the consequences of the π→π* electronic transition on the structure and microsolvation sphere of the dye has been analysed in some detail and compared to the ground state behaviour. Thereafter, fluorescence has been calculated at the TD-DFT level on configurations sampled from the simulated MD trajectories, allowing us to include time dependent solvent effects in the computed emission spectrum. The latter, when compared with the absorption spectrum, reproduces well the experimental Stokes shift, further validating the proposed multilevel computational procedure.     

Non-Born-Oppenheimer molecular dynamics of Na...FH photodissociation

The accuracy of non-Born-Oppenheimer (electronically nonadiabatic) semiclassical trajectory methods for simulations of "deep quantum" systems is reevaluated in light of recent quantum mechanical calculations of the photodissociation of the Na...FH van der Waals complex. In contrast to the conclusion arrived at in an earlier study, semiclassical trajectory methods are shown to be qualitatively accurate for this system, thus further validating their use for systems with large electronic energy gaps. Product branching in semiclassical surface hopping and decay-of-mixing calculations is affected by a region of coupling where the excited state is energetically forbidden. Frustrated hops in this region may be attributed to a failure of the treatment of decoherence, and a stochastic model for decoherence is introduced into the surface hopping method and is shown to improve the agreement with the quantum mechanical results. A modification of the decay-of-mixing method resulting in faster decoherence in this region is shown to give similarly improved results.     

An accurate study of the dynamics of the C+OH reaction on the second excited 1(4)A" potential energy surface

The dynamics of the C((3)P)+OH(X(2)Π) → CO(a(3)Π)+H((2)S) on its second excited potential energy surface, 1(4)A", have been investigated in detail by means of an accurate quantum mechanical (QM) time-dependent wave packet (TDWP) approach. Reaction probabilities for values of the total angular momentum J up to 50 are calculated and integral cross sections for a collision energy range which extends up to 0.1 eV are shown. The comparison with quasi-classical trajectory (QCT) and statistical methods reveals the important role played by the double well structure existing in the potential energy surface. The TDWP differential cross sections exhibit a forward-backward symmetry which could be interpreted as indicative of a complex-forming mechanism governing the dynamics of the process. The QM statistical method employed in this study, however, is not capable to reproduce the main features of the possible insertion nature in the reactive collision. The ability to stop individual trajectories selectively at specific locations inside the potential energy surface makes the QCT version of the statistical approach a better option to understand the overall dynamics of the process.     

Three-dimensional quantum dynamics study of vibrational predissociation of HeI_2 van der Waals molecule for low vibrational excitation using the time-dependent wave packet method

Three-dimensional quantum mechanical calculations for vibrational predissociation of HeI2(B) van der Waals molecules are presented using the time-dependent wave packet technique within the golden rule approxima tion.The total and partial decay widths,lifetimes,rates and their dependence on initial vibrational states were obtained for HeI2 at low initial vibrational excited levels.Our calculations show that the calculated tota decay widths,lifetimes and rates agree well with those extrapolated from experimental data available The predicted total decay widths as a function of initial vibrational states exhibit highly nonlinear behavior.The very short propagation time (less.than 1 ps) required in the golden rule wave packet calculation is determined by the duration time of the final state inter-action between the fragments on the vibrationally deexcited adiabatic potential surface.The final state interaction between the fragments is shown to play an important role in determining the final rotational distri     

Theoretical prediction on vibrational spectra of [Ar…Ar-H]~+

As a special substance between isolated molecules and condensed phase, clusters have drawn more and more attention by theoreticians and experimentalists. The protonated rare gas cluster is one kind of simplest clusters, which can be looked on as the simplest solution composed of the simplest solute, proton, and the simplest solvent, rare gas. The study on such a system can help us to know more about the complex condensed matter. However, the information for the molecular properties of protonat…