Resonance vibrational Raman optical activity: a time-dependent density functional theory approach

We present a method to calculate both on- and off-resonance vibrational Raman optical activities (VROAs) of molecules using time-dependent density functional theory. This is an extension of a method to calculate the normal VROA by including a finite lifetime of the electronic excited states in all calculated properties. The method is based on a short-time approximation to Raman scattering and is, in the off-resonance case, identical to the standard theory of Placzek. The normal and resonance VROA spectra are calculated from geometric derivatives of the different generalized polarizabilites obtained using linear response theory which includes a damping term to account for the finite lifetime. Gauge-origin independent results for normal VROA have been ensured using either the modified-velocity gauge or gauge-included atomic orbitals. For the resonance VROA only the modified-velocity gauge has been implemented. We present some initial results for H(2)O(2) and (S)-methyloxirane and compare with predictions from a simple two-state approximation.     

Resonance Raman scattering of rhodamine 6G as calculated using time-dependent density functional theory

In this work, we present the first calculation of the resonance Raman scattering (RRS) spectrum of rhodamine 6G (R6G) which is a prototype molecule in surface-enhanced Raman scattering (SERS). The calculation is done using a recently developed time-dependent density functional theory (TDDFT) method, which uses a short-time approximation to evaluate the Raman scattering cross section. The normal Raman spectrum calculated with this method is in good agreement with experimental results. The calculated RRS spectrum shows qualitative agreement with SERS results at a wavelength that corresponds to excitation of the S(1) state, but there are significant differences with the measured RRS spectrum at wavelengths that correspond to excitation of the vibronic sideband of S(1). Although the agreement with the experiments is not perfect, the results provide insight into the RRS spectrum of R6G at wavelengths close to the absorption maximum where experiments are hindered due to strong fluorescence. The calculated resonance enhancements are found to be on the order of 10(5). This indicates that a surface enhancement factor of about 10(10) would be required in SERS in order to achieve single-molecule detection of R6G.     

Pseudospectral time-dependent density functional theory

Time-dependent density functional theory (TDDFT) is implemented within the Tamm-Dancoff approximation (TDA) using a pseudospectral approach to evaluate two-electron repulsion integrals. The pseudospectral approximation uses a split representation with both spectral basis functions and a physical space grid to achieve a reduction in the scaling behavior of electronic structure methods. We demonstrate here that exceptionally sparse grids may be used in the excitation energy calculation, following earlier work employing the pseudospectral approximation for determining correlation energies in wavefunction-based methods with similar conclusions. The pseudospectral TDA-TDDFT method is shown to be up to ten times faster than a conventional algorithm for hybrid functionals without sacrificing chemical accuracy.     

Raman spectra of vibrational and librational modes in methane clathrate hydrates using density functional theory

The sI type methane clathrate hydrate lattice is formed during the process of nucleation where methane gas molecules are encapsulated in the form of dodecahedron (5(12)CH(4)) and tetrakaidecahedron (5(12)6(2)CH(4)) water cages. The characterization of change in the vibrational modes which occur on the encapsulation of CH(4) in these cages plays a key role in understanding the formation of these cages and subsequent growth to form the hydrate lattice. In this present work, we have chosen the density functional theory (DFT) using the dispersion corrected B97-D functional to characterize the Raman frequency vibrational modes of CH(4) and surrounding water molecules in these cages. The symmetric and asymmetric C-H stretch in the 5(12)CH(4) cage is found to shift to higher frequency due to dispersion interaction of the encapsulated CH(4) molecule with the water molecules of the cages. However, the symmetric and asymmetric O-H stretch of water molecules in 5(12)CH(4) and 5(12)6(2)CH(4) cages are shifted towards lower frequency due to hydrogen bonding, and interactions with the encapsulated CH(4) molecules. The CH(4) bending modes in the 5(12)CH(4) and 5(12)6(2)CH(4) cages are blueshifted, though the magnitude of the shifts is lower compared to modes in the high frequency region which suggests bending modes are less affected on encapsulation of CH(4). The low frequency librational modes which are collective motion of the water molecules and CH(4) in these cages show a broad range of frequencies which suggests that these modes largely contribute to the formation of the hydrate lattice.     

On correlated electron-nuclear dynamics using time-dependent density functional theory

We discuss possibilities and challenges for describing correlated electron and nuclear dynamics within a surface-hopping framework using time-dependent density functional theory (TDDFT) for the electron dynamics. We discuss the recent surface-hopping method proposed by Craig et al. [Phys. Rev. Lett. 95, 163001 (2005)] that is based on Kohn-Sham potential energy surfaces. Limitations of this approach arise due to the Kohn-Sham surfaces generally having different gradients than the true TDDFT-corrected ones. Two mechanisms of the linear response procedure cause this effect: we illustrate these with examples.     

A long-range-corrected time-dependent density functional theory

We apply the long-range correction (LC) scheme for exchange functionals of density functional theory to time-dependent density functional theory (TDDFT) and examine its efficiency in dealing with the serious problems of TDDFT, i.e., the underestimations of Rydberg excitation energies, oscillator strengths, and charge-transfer excitation energies. By calculating vertical excitation energies of typical molecules, it was found that LC-TDDFT gives accurate excitation energies, within an error of 0.5 eV, and reasonable oscillator strengths, while TDDFT employing a pure functional provides 1.5 eV lower excitation energies and two orders of magnitude lower oscillator strengths for the Rydberg excitations. It was also found that LC-TDDFT clearly reproduces the correct asymptotic behavior of the charge-transfer excitation energy of ethylene-tetrafluoroethylene dimer for the long intramolecular distance, unlike a conventional far-nucleus asymptotic correction scheme. It is, therefore, presumed that poor TDDFT results for pure functionals may be due to their lack of a long-range orbital-orbital interaction.     

All-electron time-dependent density functional theory with finite elements: time-propagation approach

We present an all-electron method for time-dependent density functional theory which employs hierarchical nonuniform finite-element bases and the time-propagation approach. The method is capable of treating linear and nonlinear response of valence and core electrons to an external field. We also introduce (i) a preconditioner for the propagation equation, (ii) a stable way to implement absorbing boundary conditions, and (iii) a new kind of absorbing boundary condition inspired by perfectly matched layers.     

Applicability of hybrid density functional theory methods to calculation of molecular hyperpolarizability

The donor/acceptor (D/A) substituted pi-conjugated organic molecules possess extremely fast nonlinear optical (NLO) response time that is purely electronic in origin. This makes them promising candidates for optoelectronic applications. In the present study, we utilized four hybrid density functionals (B3LYP, B97-2, PBE0, BMK), Hartree-Fock, and second order Moller-Plesset correlation energy correction, truncated at second-order (MP2) methods with different basis sets to estimate molecular first hyperpolarizability (beta) of D/A-substituted benzenes and stilbenes (D=OMe, OH, NMe(2), NH(2); A=NO(2), CN). The results of density functional theory (DFT) calculations are compared to those of MP2 method and to the experimental data. We addressed the following questions: (1) the accurate techniques to compare calculated results to each other and to experiment, (2) the choice of the basis set, (3) the effect of molecular planarity, and (4) the choice of the method. Comparison of the absolute values of hyperpolarizabilities obtained computationally and experimentally is complicated by the ambiguities in conventions and reference values used by different experimental groups. A much more tangible way is to compare the ratios of beta's for two (or more) given molecules of interest that were calculated at the same level of theory and measured at the same laboratory using the same conventions and reference values. Coincidentally, it is the relative hyperpolarizabilities rather than absolute ones that are of importance in the rational molecular design of effective NLO materials. This design includes prediction of the most promising candidates from particular homologous series, which are to be synthesized and used for further investigation. In order to accomplish this goal, semiquantitative level of accuracy is usually sufficient. Augmentation of the basis set with polarization and diffuse functions changes beta by 20%; however, further extension of the basis set does not have significant effect. Thus, we recommend 6-31+G(*) basis set. We also show that the use of planar geometry constraints for the molecules, which can somewhat deviate from planarity in the gas phase, leads to sufficient accuracy (with an error less than 10%) of predicted values. For all the molecules studied, MP2 values are in better agreement with experiment, while DFT hybrid methods overestimate beta values. BMK functional gives the best agreement with experiment, with systematic overestimation close to the factor of 1.4. We propose to use the scaled BMK results for prediction of molecular hyperpolarizability at semiquantitative level of accuracy.     

Efficient time-dependent density functional theory approximations for hybrid density functionals: analytical gradients and parallelization

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.     

Polarizable continuum model with the fragment molecular orbital-based time-dependent density functional theory

The polarizable continuum model (PCM) for describing the solvent effect was combined with the fragment molecular orbital-based time-dependent density functional theory (TDDFT). Several levels of the many-body expansion were implemented, and the importance of the many-body contributions to the singlet-excited states was discussed. To calibrate the accuracy, we performed a number of the model calculations using our method and the regular TDDFT in solution, applying them to phenol and polypeptides at the long-range corrected BLYP/6-31G* level. It was found that for systems up to 192 atoms the largest error in the excitation energy was 0.006 eV (vs. the regular TDDFT/PCM of the full system). The solvent shifts and the conformer effects were discussed, and the scaling was found to be nearly linear. Finally, we applied our method to the lowest singlet excitation of the photoactive yellow protein (PYP) in aqueous solution and determined the excitation energy to be in reasonable agreement with experiment. The excitation energy analysis provided the contributions of individual residues, and the main factors as well as their solvent shifts were determined.     

Continuum states from time-dependent density functional theory

Linear response time-dependent density functional theory is used to study low-lying electronic continuum states of targets that can bind an extra electron. Exact formulas to extract scattering amplitudes from the susceptibility are derived in one dimension. A single-pole approximation for scattering phase shifts in three dimensions is shown to be more accurate than static exchange for singlet electron-He(+) scattering.     

General excitations in time-dependent density functional theory

A general framework within time-dependent density functional theory is presented for the calculation of excitations to states of arbitrary multiplicity in molecular systems with a non-singlet ground state. The proposed approach combines generalized orbital excitation operators designed to generate excited states which have well-defined multiplicities and the noncollinear formulation of density functional theory and it can be straightforwardly implemented in currently existing density functional programs.     

Spin-multiplet energies from time-dependent density functional theory

Starting from a formally exact density-functional representation of the frequency-dependent linear density response and exploiting the fact that the latter has poles at the true excitation energies, we develop a density-functional method for the calculation of excitation energies. Simple additive corrections to the Kohn-Sham single-particle transition energies are derived whose actual computation only requires the ordinary static Kohn-Sham orbitals and the corresponding eigenvalues. Numerical results are presented for spin-singlet and triplet energies. © 1996 John Wiley & Sons, Inc.     

Long-range excitations in time-dependent density functional theory

Adiabatic time-dependent density functional theory fails for excitations of a heteroatomic molecule composed of two open-shell fragments at large separation. Strong frequency dependence of the exchange-correlation kernel is necessary for both local and charge-transfer excitations. The root of this is the static correlation created by the step in the exact Kohn-Sham ground-state potential between the two fragments. An approximate nonempirical kernel is derived for excited molecular dissociation curves at large separation. Our result is also relevant when the usual local and semilocal approximations are used for the ground-state potential, as static correlation there arises from the coalescence of the highest occupied and lowest unoccupied orbital energies as the molecule dissociates.     

Prediction of iron K-edge absorption spectra using time-dependent density functional theory

Iron K-edge X-ray absorption pre-edge features have been calculated using a time-dependent density functional approach. The influence of functional, solvation, and relativistic effects on the calculated energies and intensities has been examined by correlation of the calculated parameters to experimental data on a series of 10 iron model complexes, which span a range of high-spin and low-spin ferrous and ferric complexes in O(h) to T(d) geometries. Both quadrupole and dipole contributions to the spectra have been calculated. We find that good agreement between theory and experiment is obtained by using the BP86 functional with the CP(PPP) basis set on the Fe and TZVP one of the remaining atoms. Inclusion of solvation yields a small improvement in the calculated energies. However, the inclusion of scalar relativistic effects did not yield any improved correlation with experiment. The use of these methods to uniquely assign individual spectral transitions and to examine experimental contributions to backbonding is discussed.     

Theoretical study of the benzene excimer using time-dependent density functional theory

A theoretical characterization of the potential energy surfaces of the singlet benzene excimer states derived from the B2u monomer excited state has been performed using time-dependent density functional theory. The excited-state potential energy surfaces were initially characterized by computations along the parallel and perpendicular intermolecular translational coordinates. These calculations predict that the lowest excited state for parallel translation is bound with a minimum at 3.15 angstroms and with a binding energy of 0.46 eV, while the perpendicular translational coordinate was essentially found to be a repulsive state. At the calculated minimum distance, the effect of in-plane rotation, out-of-plane rotation, and slipped-parallel translation were examined. The rotational calculations predict that deviations from the D6h geometry lead to a destabilization of the excimer state; however, small angular variations in the range of 0 degrees -10 degrees are predicted to be energetically feasible. The slipped-parallel translational calculations also predict a destabilizing effect on the excimer state and were found to possess barriers to this type of dissociation in the range of 0.50-0.61 eV. When compared to experimentally determined values for the benzene excimer energetics, the calculated values were found to be in semiquantitative agreement. Overall, this study suggests that the time-dependent density functional theory method can be used to characterize the potential energy surfaces and the energetics of aromatic excimers with reasonable accuracy.     

Resonance Raman spectra of uracil based on Kramers-Kronig relations using time-dependent density functional calculations and multireference perturbation theory

The use of time-dependent density functional calculations for the optimization of excited-state structures and the subsequent calculation of resonance Raman intensities within the transform-theory framework is compared to calculations of Hartree-Fock/configuration interaction singles-type (CIS). The transform theory of resonance Raman scattering is based on Kramers-Kronig relations between polarizability tensor components and the optical absorption. Stationary points for the two lowest excited singlet states of uracil are optimized and characterized by means of numerical differentiation of analytical excited-state gradients. It is shown that the effect of electron correlation leads to substantial modifications of the relative intensities. Calculations of vibrational frequencies for ground and excited states are carried out, which show that the neglect of Duschinsky mixing and the assumption of equal wave numbers for ground and excited state are not in all cases good approximations. We also compare the transform-theory resonance Raman intensities with those obtained within a simple approximation from excited-state gradients at the ground-state equilibrium position, and find that they are in qualitative agreement in the case of CIS, but show some important differences in calculations based on density functional theory. Since the results from CIS calculations are in better agreement with experiment, we also present approximate resonance Raman spectra obtained using excited-state gradients from multireference perturbation theory calculations, which confirm the CIS gradients.     

Anharmonic analysis of the vibrational spectrum of ketene by density functional theory using second-order perturbative approach

The paper reports main results of a comprehensive study of the vibrational spectrum of ketene computed using second-order perturbation theory treatment based on quartic, cubic and semidiagonal quartic force constants. Two different models--a homogeneous model using the same density functionals and basis functions for the harmonic calculations and anharmonic corrections, and a hybrid model in which the two parts of the calculation are conducted using different density functionals and basis sets--have been employed in the present calculations. Different DFT and CCSD methods and DZ and TZ extended basis sets involving diffuse and polarization functions have been used to calculate optimized and vibrationally averaged geometrical parameters, the harmonic and anharmonic vibrational frequencies and the spectroscopic constants such as anharmonicity constants, rotational constants, rotation-vibration coupling constants, Nielsen's centrifugal distortion constants and Coriolis coupling constants. Homogeneous model is found to be superior to the hybrid model in several respects. Difficulties in the hybrid model may arise due to one of the following reasons: (a) the basic requirement that the geometry optimization and frequency calculations must be done at the same level of theory to have valid frequencies is not met in the hybrid model; (b) the molecular structure gets reoptimized at the low level for anharmonic corrections; (c) in addition, the perturbation could also diverge for the above reasons, particularly for the very low, very anharmonic terms where the harmonic approximation is not close enough to make the perturbation work.     

Theoretical investigation of the molecular structure,vibrational spectra,and molecular docking of tramadol using density functional theory

The optimized molecular structures, harmonic vibrational wavenumbers, and the corresponding vibrational assignments of (1S,2S)-tramadol and (1R,2R)-tramadol are computationally examined using the B3LYP density functional theory method together with the standard 6–311++G(d,p) and def2-TVZP basis sets. The optimized structures show that phenolic rings of both 1R,2R and 1S,2S tramadol adopt planar geometry, which are slightly distorted due to the substitution at the meta-position; and the six-membered cyclohexane adopts a slightly distorted chair conformation. The 1S,2S enantiomer is energetically more favorable than 1R,2R with the energy differences of 1.32 and 1.03 kcal/mol obtained at B3LYP/6–311++G(d,p) and B3LYP/Def2-TVZP levels, respectively. The analysis of the binding pocket in the silico molecular docking with the m-opioid receptor shows that it originated two clusters with the 1S,2S enantiomer and one cluster with the 1R,2R enantiomer of tramadol. The results point to a more stable complex of the m-opioid receptor with the 1R,2R enantiomer of tramadol.     

Real-time time-dependent density functional theory using density fitting and the continuous fast multipole method

An implementation of real-time time-dependent density functional theory (RT-TDDFT) within the TURBOMOLE program package is reported using Gaussian-type orbitals as basis functions, second and fourth order Magnus propagator, and the self-consistent field as well as the predictor–corrector time integration schemes. The Coulomb contribution to the Kohn–Sham matrix is calculated combining density fitting approximation and the continuous fast multipole method. Performance of the implementation is benchmarked for molecular systems with different sizes and dimensionalities. For linear alkane chains, the wall time for density matrix time propagation step is comparable to the Kohn-Sham (KS) matrix construction. However, for larger two- and three-dimensional molecules, with up to about 5,000 basis functions, the computational effort of RT-TDDFT calculations is dominated by the KS matrix evaluation. In addition, the maximum time step is evaluated using a set of small molecules of different polarities. The photoabsorption spectra of several molecular systems calculated using RT-TDDFT are compared to those obtained using linear response time-dependent density functional theory and coupled cluster methods.