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Computational modeling of plasmon-mediated molecular photophysical and photochemical behaviors can help us better understand and tune the bound molecular properties and reactivity and make better decisions to design and control nanostructures. However, computational investigations of coupled plasmon–molecule systems are challenging due to the lack of accurate and efficient protocols to simulate these systems. Here, we present a hybrid scheme by combining the real-time time-dependent density functional theory (RT-TDDFT) approach with the time-domain frequency dependent fluctuating charge (TD-ωFQ) model. At first, we transform ωFQ in the frequency-domain, an atomistic electromagnetic model for the plasmonic response of plasmonic metal nanoparticles (PMNPs), into the time-domain and derive its equation-of-motion formulation. The TD-ωFQ introduces the nonequilibrium plasmonic response of PMNPs and atomistic interactions to the electronic excitation of the quantum mechanical (QM) region. Then, we combine TD-ωFQ with RT-TDDFT. The derived RT-TDDFT/TD-ωFQ scheme allows us to effectively simulate the plasmon-mediated "real-time" electronic dynamics and even the coupled electron–nuclear dynamics by combining them with the nuclear dynamics approaches. As a first application of the RT-TDDFT/TD-ωFQ method, we study the nonradiative decay rate and plasmon-enhanced absorption spectra of two small molecules in the proximity of sodium MNPs. Thanks to the atomistic nature of the ωFQ model, the edge effect of MNP on absorption enhancement has also been investigated and unveiled. [ABSTRACT FROM AUTHOR]

The nonadiabatic phenomena, which are characterized by a strong coupling between electronic and nuclear motions, are ubiquitous. The nonadiabatic effect of the studied system can be significantly affected by the surrounding environment, such as solvents, in which such nonadiabatic process takes place. It is essential to develop the theoretical models to simulate these processes while accurately modeling the solvent environment. The time-dependent density functional theory (TDDFT) is currently the most efficient approach to describe the electronic structures and dynamics of complex systems, while the polarizable continuum model (PCM) represents one of the most successful examples among continuum solvation models. Here, we formulate the first-order derivative couplings (DCs) between the ground and excited states as well as between two excited states by utilizing time-independent equation of motion formalism within the framework of both linear response and spin flip formulations of TDDFT/CPCM (the conductor-like PCM), and implement the analytical DCs into the Q-CHEM electronic structure software package. The analytic implementation is validated by the comparison of the analytical and finite-difference results, and reproducing geometric phase effect in the protonated formaldimine test case. Taking 4-(N,N-dimethylamino)benzonitrile and uracil in the gas phase and solution as an example, we demonstrate that the solvent effect is essential not only for the excitation energies of the low-lying excited-states but also for the DCs between these states. Finally, we calculate the internal conversion rate of benzophenone in a solvent with DC being used. The current implementation of analytical DCs together with the existing analytical gradient and Hessian of TDDFT/PCM excited states allows one to study the nonadiabatic effects of relatively large systems in solutions with low computational cost. [ABSTRACT FROM AUTHOR]

This work is devoted to deriving and implementing analytic second- and third-order energy derivatives with respect to the nuclear coordinates and external electric field within the framework of the hybrid quantum mechanics/molecular mechanics method with induced charges and dipoles (QM/DIM). Using these analytic energy derivatives, one can efficiently compute the harmonic vibrational frequencies, infrared (IR) and Raman scattering (RS) spectra of the molecule in the proximity of noble metal clusters/nanoparticles. The validity and accuracy of these analytic implementations are demonstrated by the comparison of results obtained by the finite-difference method and the analytic approaches and by the full QM and QM/DIM calculations. The complexes formed by pyridine and two sizes of gold clusters (Au18 and Au32) at varying intersystem distances of 3, 4, and 5 Å are used as the test systems, and Raman spectra of 4,4′-bipyridine in the proximity of Au2057 and Ag2057 metal nanoparticles (MNP) are calculated by the QM/DIM method and compared with experimental results as well. We find that the QM/DIM model can well reproduce the IR spectra obtained from full QM calculations for all the configurations, while although it properly enhances some of the vibrational modes, it artificially overestimates RS spectral intensities of several modes for the systems with very short intersystem distance. We show that this could be improved, however, by incorporating the hyperpolarizability of the gold metal cluster in the evaluation of RS intensities. Additionally, we address the potential impact of charge migration between the adsorbate and MNPs. [ABSTRACT FROM AUTHOR]

Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin–orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm–Dancoff approximation to TDDFT, spin–flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine–Ag20 complex), we emphasize that caution is needed to properly account for system–environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments. [ABSTRACT FROM AUTHOR]

The vibrationally resolved absorption spectra of zinc phthalocyanine (ZnPc) aggregates (up to 70 monomers) are explored using the non-Markovian stochastic Schrödinger equation. Various types of local excitations, charge-transfer (CT) excitations, and exciton–phonon couplings are explicitly included in a comprehensive model Hamiltonian, which is parameterized by first-principles calculations. The absorption spectral simulations clarify that the two absorption bands in the Q-band region observed in experiments can be assigned to the contribution from the CT-mediated interactions, rather than the mixtures of different-type aggregates, as prevailingly assumed. Furthermore, the relative intensities of the two bands are found to be closely related to the intermolecular distance and molecular number in a ZnPc aggregate. From the investigation of the decoherence process after optical excitation, it is found that CT states can induce coherence regeneration as the time scale of charge separation is much faster than that of the vibration-induced decoherence. However, they would instead boost the decoherence process as the two time scales become comparable. The two different effects of CT states may suggest a novel way to regulate the decoherence process in excitation energy relaxation. [ABSTRACT FROM AUTHOR]

The nonlinear optical properties of hybrid systems composed of a silver nanosphere and an open-ended finite-sized armchair single-walled carbon nanotube (SWCNT) are systematically investigated by the hybrid time-dependent Hartree–Fock (TDHF)/finite difference time domain (FDTD) approach, which combines the real-time TDHF approach for the molecular electronic dynamics with the classical computational electrodynamics approach, the FDTD, for solving Maxwell's equations. The high order harmonic generation (HHG) spectra of SWCNTs are studied as a function of the intensity (I0) and frequency (ω0) of the incident field, and SWCNTs length as well. It is found that the near field generated by a Ag nanoparticle has an overall enhancement to the molecular HHG in all the energy range, and it extends the HHG spectra to high energy. The inhomogeneity of the near field results in the appearance of even-order harmonics, and their corresponding spectral intensities are sensitive to ω0, therefore the near field's gradient. When ω0 is far away from the frequency of plasmon resonance of the silver nanosphere (ωc), the interference between the incident and scattering light beams extends the spectral range and makes the HHG spectra more sensitive to I0, while at ω0 = ωc, the impact of the interference on the spectra is negligible. [ABSTRACT FROM AUTHOR]

The complex interplay between molecules and plasmonic metal nanoparticles (MNPs) presents a set of particular characteristics in absorption/scattering spectra such as excitonic splitting, asymmetric line shapes, plasmon-induced absorption enhancement and transparencies, etc. Although the MNP-molecule systems have been intensively investigated experimentally and theoretically, the construction of a theoretical framework which can produce all the disparate experimental observations and account for the electron-phonon (e-p) coupling is still in progress. Here, we present a theoretical approach which can account for both the plasmon-exciton coupling and the e-p interaction and produce all the spectral line shapes ranging from Fano antiresonance to Rabi splitting by simply tuning the coupling strength or plasmon damping rate. Additionally, we demonstrate the evolution of vibronic spectra and exciton dynamics with the coupling strength, plasmon damping rate, and detuning energy. It is found that the vibronic structures appearing in Rabi-like spectra are worse resolved, wider, and more largely shifted than those appearing in the Fano regime, attributed to the more significant deformation of the molecular vibrational wavepacket in the Rabi-like regime than that in the Fano regime as the molecular e-p interaction increases. The positive/negative value of detuning energy can induce different degrees of the vibrational wavepacket deformation and subsequently a different effect on the spectra in different coupling regimes. [ABSTRACT FROM AUTHOR]

It has been widely recognized that plasmonic metal nanoparticles (MNPs) can enhance the power convention efficiency (PCE) of dye-sensitized solar cells (DSSCs). This enhancement is ascribed to the combined effects of plasmon decay, scattering, near-field enhancement, and exciting charge carriers in semiconductors through plasmon-induced resonance energy transfer (PIRET) and hot electron injection (HEI). PIRET and HEI processes appeared between MNPs, and semiconductors have been intensively investigated; however, it is not clear how the collaborative effect of PIRET and photon-induced direct and indirect electron transfer (PICT) occurred between plasmonic metals and dyes, and the interference of different charge separation channels (CSCs) starting from PIRET and PICT affects the PCE of DSSCs. This work aims to address these issues. We apply a model Hamiltonian method, which obviously includes both PIRET and PICT processes from Au MNP to dye molecules and incorporates the dye's electron-phonon interaction, to investigate the carrier dynamics. It is found that PIRET deforms the wavepacket dynamics of the molecular excited state and results in ten-fold enhancement of dye absorption. MNPs augment light absorption and increase the electron density in empty molecular orbitals of the dye molecule. Consequently, this enhances the interfacial charge separation. Furthermore, we observed the interference behavior of two CSCs and gave a full-scale insight into the correlation between the constructive/destructive interference and the electronic-state properties as well as carrier-phonon interactions. This work provides a theoretical guidance to optimize DSSCs. [ABSTRACT FROM AUTHOR]

The paper presents the formalism, implementation, and performance of the analytical approach for the excited-state Hessian in the time-dependent density functional theory (TDDFT) that extends our previous work [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011)] on the analytical Hessian in TDDFT within Tamm-Dancoff approximation (TDA) to full TDDFT. In contrast to TDA-TDDFT, an appreciable advantage of full TDDFT is that it maintains the oscillator strength sum rule, and therefore yields more precise results for the oscillator strength and other related physical quantities. For the excited-state harmonic vibrational frequency calculation, however, full TDDFT does not seem to be advantageous since the numerical tests demonstrate that the accuracy of TDDFT with and without TDA are comparable to each other. As a common practice, the computed harmonic vibrational frequencies are scaled by a suitable scale factor to yield good agreement with the experimental fundamental frequencies. Here we apply both the optimized ground-state and excited-state scale factors to scale the calculated excited-state harmonic frequencies and find that the scaling decreases the root-mean-square errors. The optimized scale factors derived from the excited-state calculations are slightly smaller than those from the ground-state calculations. [ABSTRACT FROM AUTHOR]

A method in time domain is proposed to investigate resonance Raman spectra of absorbed molecules on semiconductor surfaces. The charge transfer at the molecule-surface interface is incorporated with the use of an Anderson-Newns type Hamiltonian, where the surface continuum state is dealt with an expansion of Legendre polynomials for fast numerical convergence. From a model test, it is found that the intensities of Raman modes in the sole molecule generally decrease as the molecule-surface interaction is switched on, except that the energy gaps between the molecular excited state and the bottom of the band are at special values. New Raman peaks which are not observed in the sole molecule, however, appear and are greatly enhanced. The enhancement depends on the electronic coupling and the energy gap. It is also highly sensitive to the mode-specific reorganization energy in the charge transfer state, and a thousand times enhancement can be obtained at a certain reorganization energy. The corresponding electron dynamics is revealed by the population decay from the absorbed molecule. [ABSTRACT FROM AUTHOR]

We present the analytical expression and computer implementation for the second-order energy derivatives of the electronic excited state with respect to the nuclear coordinates in the time-dependent density functional theory (TDDFT) with Gaussian atomic orbital basis sets. Here, the Tamm-Dancoff approximation to the full TDDFT is adopted, and therefore the formulation process of TDDFT excited-state Hessian is similar to that of configuration interaction singles (CIS) Hessian. However, due to the replacement of the Hartree-Fock exchange integrals in CIS with the exchange-correlation kernels in TDDFT, many quantitative changes in the derived equations are arisen. The replacement also causes additional technical difficulties associated with the calculation of a large number of multiple-order functional derivatives with respect to the density variables and the nuclear coordinates. Numerical tests on a set of test molecules are performed. The simulated excited-state vibrational frequencies by the analytical Hessian approach are compared with those computed by CIS and the finite-difference method. It is found that the analytical Hessian method is superior to the finite-difference method in terms of the computational accuracy and efficiency. The numerical differentiation can be difficult due to root flipping for excited states that are close in energy. TDDFT yields more exact excited-state vibrational frequencies than CIS, which usually overestimates the values. [ABSTRACT FROM AUTHOR]

A new formulation of the diagonalization step in self-consistent-field (SCF) electronic structure calculations is presented. It exactly replaces the diagonalization of the effective Hamiltonian with the solution of a set of second order nonlinear equations. The density matrix and/or the new set of occupied orbitals can be directly obtained from the resulting solution. This formulation may offer interesting possibilities for new approaches to efficient SCF calculations. The working equations can be derived either from energy minimization with respect to a Cayley-type parametrization of a unitary matrix, or from a similarity transformation approach. [ABSTRACT FROM AUTHOR]

A variety of chemical systems exhibit multiple reaction pathways that adjoin to a common reactant state. In fact, any reaction producing side products or proceeding via a stable intermediate involves a species possessing at least two reaction pathways. Despite improvements in ab initio transition-state search algorithms it remains difficult to detect multiple reaction pathways. Typically, multiple reaction pathways can only be detected by intuitively varying the initial point in the transition-state search trajectory. This reliance on intuition limits the ability to discover new and unexpected chemistry using ab initio methods. This paper proposes a systematic and intuition-free method for biasing a transition-state search to identify multiple reaction pathways originating from a common reactant state. The method allows the successive location of transition states, with each successful search contributing to a cumulative bias potential for the following search. The method is applicable to all psuedo-Newton-Raphson-type transition-state searches. The procedure was tested for a model potential energy surface and for the thermal rearrangement of trans-1,4-dimethylcyclobutene. In the latter case, four reaction pathways were discovered: two exothermic conrotatory ring openings leading to hexadienes, an endothermic methyl migration pathway leading to a carbene, and an exothermic rearrangement leading to 3-methyl-1,4-pentadiene. In accordance with experiment, the calculations predict that the conrotatory pathway leading to trans,trans-2,4-hexadiene is the kinetically dominant pathway. The methodology was also used to compute selectivities for competitive pathways producing trans and cis triflouropentadiene products in the thermal rearrangement of 3-triflouromethyl-cyclobutene. Again, results were in accord with experimental observations. [ABSTRACT FROM AUTHOR]

This work extends our previous works [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011); J. Liu and W. Z. Liang, J. Chem. Phys. 135, 184111 (2011)] on analytical excited-state Hessian within the framework of time-dependent density functional theory (TDDFT) to couple with a conductor-like polarizable continuum model (CPCM). The formalism, implementation, and application of analytical first and second energy derivatives of TDDFT/CPCM excited state with respect to the nuclear and electric perturbations are presented. Their performances are demonstrated by the calculations of excitation energies, excited-state geometries, and harmonic vibrational frequencies for a number of benchmark systems. The calculated results are in good agreement with the corresponding experimental data or other theoretical calculations, indicating the reliability of the current computer implementation of the developed algorithms. Then we made some preliminary applications to calculate the resonant Raman spectrum of 4-hydroxybenzylidene-2,3-dimethyl-imidazolinone in ethanol solution and the infrared spectra of ground and excited states of 9-fluorenone in methanol solution. [ABSTRACT FROM AUTHOR]

Absorption spectrum of recently discovered single-walled 4 Å carbon nanotubes is measured. The semiempirical PM3 localized-density-matrix method is employed to evaluate the absorption spectra of three possible 4 Å single-walled carbon nanotubes, (3,3), (4,2), and (5,0). Both experimental and calculated results reveal that these nanotubes have finite optical gaps and strong anisotropic optical responses. When the electric field is perpendicular to the nanotubes, they are transparent to visible lights; and this is confirmed and explained by the calculations. Compared to the measured absorption spectrum, calculated absorption spectra are used to determine the chirality of the nanotubes synthesized in the channels of porous zeolites. [ABSTRACT FROM AUTHOR]

The linear scaling localized-density-matrix (LDM) method is generalized to calculate the nonlinear optical responses of large polyacetylene oligomers. The ground state reduced single-electron density matrix is initialized by the divide-and-conquer approach and is obtained subsequently using the LDM method. The third-harmonic generation spectra of large oligomers are calculated. The saturation of off-resonant second hyperpolarizability χ[sup (3)](0) has been reinvestigated, and the value of χ[sup (3)](0) is found to depend mainly on the optical gap and the number of double bonds. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Computational modeling of plasmon-mediated molecular photophysical and photochemical behaviors can help us better understand and tune the bound molecular properties and reactivity and make better decisions to design and control nanostructures. However, computational investigations of coupled plasmon-molecule systems are challenging due to the lack of accurate and efficient protocols to simulate these systems. Here, we present a hybrid scheme by combining the real-time time-dependent density functional theory (RT-TDDFT) approach with the time-domain frequency dependent fluctuating charge (TD-ωFQ) model. At first, we transform ωFQ in the frequency-domain, an atomistic electromagnetic model for the plasmonic response of plasmonic metal nanoparticles (PMNPs), into the time-domain and derive its equation-of-motion formulation. The TD-ωFQ introduces the nonequilibrium plasmonic response of PMNPs and atomistic interactions to the electronic excitation of the quantum mechanical (QM) region. Then, we combine TD-ωFQ with RT-TDDFT. The derived RT-TDDFT/TD-ωFQ scheme allows us to effectively simulate the plasmon-mediated "real-time" electronic dynamics and even the coupled electron-nuclear dynamics by combining them with the nuclear dynamics approaches. As a first application of the RT-TDDFT/TD-ωFQ method, we study the nonradiative decay rate and plasmon-enhanced absorption spectra of two small molecules in the proximity of sodium MNPs. Thanks to the atomistic nature of the ωFQ model, the edge effect of MNP on absorption enhancement has also been investigated and unveiled., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

The time-dependent correlation function approach for the calculations of absorption and resonance Raman spectra (RRS) of organic molecules absorbed on semiconductor surfaces [Y. Zhao and W. Z. Liang, J. Chem. Phys. 135, 044108 (2011)] is extended to include the contribution of the intermolecular charge transfer (CT) excitation from the absorbers to the semiconducting nanoparticles. The results demonstrate that the bidirectionally interfacial CT significantly modifies the spectral line shapes. Although the intermolecular CT excitation makes the absorption spectra red shift slightly, it essentially changes the relative intensities of mode-specific RRS and causes the oscillation behavior of surface enhanced Raman spectra with respect to interfacial electronic couplings. Furthermore, the constructive and destructive interferences of RRS from the localized molecular excitation and CT excitation are observed with respect to the electronic coupling and the bottom position of conductor band. The interferences are determined by both excitation pathways and bidirectionally interfacial CT.

The time-dependent density functional theory (TDDFT) has become the most popular method to calculate the electronic excitation energies, describe the excited-state properties, and perform the excited-state geometric optimization of medium and large-size molecules due to the implementation of analytic excited-state energy gradient and Hessian in many electronic structure software packages. To describe the molecules in condensed phase, one usually adopts the computationally efficient hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) models. Here, we extend our previous work on the energy gradient of TDDFT/MM excited state to account for the mutual polarization effects between QM and MM regions, which is believed to hold a crucial position in the potential energy surface of molecular systems when the photoexcitation-induced charge rearrangement in the QM region is drastic. The implementation of a simple polarizable TDDFT/MM (TDDFT/MMpol) model in Q-Chem/CHARMM interface with both the linear response and the state-specific features has been realized. Several benchmark tests and preliminary applications are exhibited to confirm our implementation and assess the effects of different treatment of environmental polarization on the excited-state properties, and the efficiency of parallel implementation is demonstrated as well.

The time-dependent wavepacket diffusive method [X. Zhong and Y. Zhao, J. Chem. Phys. 138, 014111 (2013)] is extended to investigate the energy relaxation and separation of a hot electron-hole pair in organic aggregates with incorporation of Coulomb interaction and electron-phonon coupling. The pair initial condition generated by laser pulse is represented by a Gaussian wavepacket with a central momentum. The results reveal that the hot electron energy relaxation is very well described by two rate processes with the fast rate much larger than the slow one, consistent with experimental observations, and an efficient electron-hole separation is accomplished accompanying the fast energy relaxation. Furthermore, although the extra energy indeed helps the separation by overcoming the Coulomb interaction, the width of initial wavepacket is much sensitive to the separation efficiency and the narrower wavepacket generates the more separated charges. This behavior may be useful to understand the experimental controversy of the hot carrier effect on charge separation.

This work extends our previous works [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011); J. Liu and W. Z. Liang, J. Chem. Phys. 135, 184111 (2011)] on analytical excited-state energy Hessian within the framework of time-dependent density functional theory (TDDFT) to couple with molecular mechanics (MM). The formalism, implementation, and applications of analytical first and second energy derivatives of TDDFT/MM excited state with respect to the nuclear and electric perturbations are presented. Their performances are demonstrated by the calculations of adiabatic excitation energies, and excited-state geometries, harmonic vibrational frequencies, and infrared intensities for a number of benchmark systems. The consistent results with the full quantum mechanical method and other hybrid theoretical methods indicate the reliability of the current numerical implementation of developed algorithms. The computational accuracy and efficiency of the current analytical approach are also checked and the computational efficient strategies are suggested to speed up the calculations of complex systems with many MM degrees of freedom. Finally, we apply the current analytical approach in TDDFT/MM to a realistic system, a red fluorescent protein chromophore together with part of its nearby protein matrix. The calculated results indicate that the rearrangement of the hydrogen bond interactions between the chromophore and the protein matrix is responsible for the large Stokes shift.

A time-dependent approach is presented to simulate the two-photon absorption (TPA) and resonance hyper-Raman scattering (RHRS) spectra including Duschinsky rotation (mode-mixing) and Herzberg-Teller (HT) vibronic coupling effects. The computational obstacles for the excited-state geometries, vibrational frequencies, and nuclear derivatives of transition dipole moments, which enter the expressions of TPA and RHRS cross sections, are further overcome by the recently developed analytical excited-state energy derivative approaches in the framework of time-dependent density functional theory. The excited-state potential curvatures are evaluated at different levels of approximation to inspect the effects of frequency differences, mode-mixing and HT on TPA and RHRS spectra. Two types of molecules, one with high symmetry (formaldehyde, p-difluorobenzene, and benzotrifluoride) and the other with non-centrosymmetry (cis-hydroxybenzylidene-2,3-dimethylimidazolinone in the deprotonated anion state (HDBI(-))), are used as test systems. The calculated results reveal that it is crucial to adopt the exact excited-state potential curvatures in the calculations of TPA and RHRS spectra even for the high-symmetric molecules, and that the vertical gradient approximation leads to a large deviation. Furthermore, it is found that the HT contribution is evident in the TPA and RHRS spectra of HDBI(-) although its one- and two-photon transitions are strongly allowed, and its effect results in an obvious blueshift of the TPA maximum with respect to the one-photon absorption maximum. With the HT and solvent effects getting involved, the simulated blueshift of 1291 cm(-1) agrees well with the experimental measurement.

Combining first-principles calculations and non-Condon charge transfer rates proposed by us recently [Y. Zhao and W. Z. Liang, J. Chem. Phys. 130, 034111 (2009)], we investigated non-Condon effect on charge carrier mobility of organic semiconductor dithiophene-tetrathiafulvalene (DT-TTF) crystal. The first-principles results reveal that only several high-frequency intramolecular vibrational modes dominate the reorganization energy, and the nuclear-coordinate dependence of electronic coupling prefers to perform an exponential or Gaussian property for most intermolecular modes rather than a linear one as assumed in conventional models. Furthermore, the electronic coupling of an isolated DT-TTF dimer is indeed affected by the surrounding molecules. The predicted non-Condon mobilities with use of the obtained structure parameters are always greater than those from Condon approximation, and the non-Condon dynamic disorder is not important for DT-TTF, which is also confirmed by molecular dynamics simulation. More interestingly, the bandlike property can be predicted under the hopping mechanism when the nuclear tunneling is incorporated.

Rigorous expressions for the calculation of nonadiabatic electron transfer rates are presented in closed forms for donor-acceptor systems incorporated fluctuating bridges and their non-Condon electronic couplings. In high temperature limit, they show a similar property to the Marcus formula. However, the Marcus parabolic with respect to the driving force is shifted for the exponential coupling while it becomes an overlap of several Gaussian functions for the linear coupling. Furthermore, the effective couplings are exponentially and linearly dependent on temperature and the squared frequencies of bridge modes for the exponential and linear couplings, respectively.

By means of the time-dependent density functional theory, the authors study the torsional dynamics of the lowest singlet electronic excited state (S1) of a bichromophoric molecule, 2-(9-anthryl)-1H-imidazo [4,5-f]-phenanthroline (AIP). The intramolecular dynamical relaxation process, the S1 potential energy surface, and the vibrationally resolved electronic absorption and fluorescence spectra are estimated. The results reveal that the strong electron-nuclear coupling leads to a dynamic structural distortion in S1 state so that the mirror-image symmetry of absorption and fluorescence spectra of AIP breaks down. The torsional motion between the donor and acceptor moieties in AIP favors the intramolecular electronic energy transfer process. The transfer rate is dominated by the relaxation time along S1 low-frequency torsional motion.

The nonadiabatic transition state theory proposed recently by Zhao et al. [J. Chem. Phys. 121, 8854 (2004)] is extended to calculate rate constants of complex systems by using the Monte Carlo and umbrella sampling methods. Surface hopping molecular dynamics technique is incorporated to take into account the dynamic recrossing effect. A nontrivial benchmark model of the nonadiabatic reaction in the condensed phase is used for the numerical test. It is found that our semiclassical results agree well with those produced by the rigorous quantum mechanical method. Comparing with available analytical approaches, we find that the simple statistical theory proposed by Straub and Berne [J. Chem. Phys. 87, 6111 (1987)] is applicable for a wide friction region although their formula is obtained using Landau-Zener [Phys. Z. Sowjetunion 2, 46 (1932); Proc. R. Soc. London, Ser. A 137, 696 (1932)] nonadiabatic transition probability along a one-dimensional diffusive coordinate. We also investigate how the nuclear tunneling events affect the dependence of the rate constant on the friction.

Based on self-consistent-field (SCF) perturbation theory, we recast the SCF and the coupled-perturbed SCF (CPSCF) equations for time-independent molecular properties into the atomic-orbital basis. The density matrix and the perturbed density matrix are obtained iteratively by solving linear equations. Only matrix multiplications and additions are required, and this approach can exploit sparse matrix multiplications and thereby offer the possibility of evaluating second-order properties in computational effort that scales linearly with system size. Convergence properties are similar to conventional molecular-orbital-based CPSCF procedures, in terms of the number of derivative Fock matrices that must be constructed. We also carefully address the issue of the numerical accuracy of the calculated second derivatives of the energy, in order to specify the minimum precision necessary in the CPSCF procedure. It is found that much looser tolerances for the perturbed density matrices are adequate when using an expression for the second derivatives that is correct through second order in the CPSCF error.

We present here three new algorithms (one purely iterative and two DIIS-like [Direct Inversion in the Iteractive Subspace]) to compute maxima of homogeneous functions of orthogonal matrices. These algorithms revolve around the mathematical lemma that, given an invertible matrix A, the function f(U)=Tr(AU) has exactly one local (and global) maximum for U special orthogonal [i.e., UU(T)=1 and det(U)=1]. This is proved in the Appendix. One application of these algorithms is the computation of localized orbitals, including, for example, Boys and Edmiston-Ruedenberg (ER) orbitals. The Boys orbitals are defined as the set of orthonormal orbitals which, for a given vector space of orbitals, maximize the sum of the distances between orbital centers. The ER orbitals maximize total self-interaction energy. The algorithm presented here computes Boys orbitals roughly as fast as the traditional method (Jacobi sweeps), while, for large systems, it finds ER orbitals potentially much more quickly than traditional Jacobi sweeps. In fact, the required time for convergence of our algorithm scales quadratically in the region of a few hundred basis functions (though cubicly asymptotically), while Jacobi sweeps for the ER orbitals traditionally scale as the number of occupied orbitals to the fifth power. As an example of the utility of the method, we provide below the ER orbitals of nitrated and nitrosated benzene, and we discuss the chemical implications.