Study of static and dynamic first hyperpolarizabilities using time-dependent density functional quadratic response theory with local contribution and natural bond orbital analysis

We apply time-dependent density-functional quadratic response theory to investigate the static and dynamic second-order polarizabilities (first hyperpolarizability) beta. A new implementation using Slater-type basis functions, numerical integration, and density fitting techniques is reported. The second order coupled perturbed Kohn-Sham equations are solved and the second-order perturbed charge density is obtained. It is useful to highlight atomic and bond contributions to understand the relation between molecular structure and properties. Four moderately sized molecules (para-nitroaniline and derivatives thereof) are investigated to assess the accuracy of the time-dependent density-functional theory computations and to investigate the distribution of the second-order charge density as well as the "beta density." Our results highlight the contributions from atoms and bonds on different functional groups to the total value of beta with Mulliken-type and natural bond orbital (NBO) analyses, and demonstrate in some cases how contributions from a particular bond may be identified easily by visual inspection of the beta density. In addition, the position of side group substitution on carbon-carbon bonds significantly affects the hyperpolarizability. A contribution analysis as performed here might be helpful for the design of new materials with desired properties.     

Inclusion of thymol into cucurbiturils: density functional theory approach with dispersion correction and natural bond orbital analysis

Journal of Inclusion Phenomena and Macrocyclic Chemistry - Stability of inclusion complexes of thymol (a natural flavour) with cucurbit[n]urils was interpreted by using density functional theory...     

The local orbital energy and density functional theory

From the viewpoint of density functional theory, an expression is derived which improves the average energy of a trial density. Applications to atoms and molecules are made using wave function methods and are based on properties of the variance, which is defined as $ (\overline {\varepsilon ^2 } - (\overline \varepsilon)^2)^{1/2} $, where ? is the local orbital energy. Calculated results for both Hartree-Fock and correlated wave functions are quite encouraging.     

Polarizability and second hyperpolarizability evaluation of long molecules by the density functional theory with long-range correction

Polarizabilities and second hyperpolarizabilities of polyacetylene and a hydrogen chain are evaluated by density functional theory (DFT) using a hybrid generalized gradient approximation functional with correct long-range electron-electron interactions. The well known catastrophic overestimate of the hyperpolarizabilities for molecular systems of enhanced length is corrected by the two-electron repulsion operator decomposition technique, integrating the distance-dependent nonlocal exchange effects for long-range interaction, while neither the asymptotically corrected exchange functional for long-range interaction nor ordinary hybrid methods seem to be capable of overcoming the serious drawback of the DFT in polarizability/hyperpolarizability evaluation.     

Optical rotation calculated with time-dependent density functional theory: the OR45 benchmark

Time-dependent density functional theory (TDDFT) computations are performed for 42 organic molecules and three transition metal complexes, with experimental molar optical rotations ranging from 2 to 2 × 10(4) deg cm(2) dmol(-1). The performances of the global hybrid functionals B3LYP, PBE0, and BHLYP, and of the range-separated functionals CAM-B3LYP and LC-PBE0 (the latter being fully long-range corrected), are investigated. The performance of different basis sets is studied. When compared to liquid-phase experimental data, the range-separated functionals do, on average, not perform better than B3LYP and PBE0. Median relative deviations between calculations and experiment range from 25 to 29%. A basis set recently proposed for optical rotation calculations (LPol-ds) on average does not give improved results compared to aug-cc-pVDZ in TDDFT calculations with B3LYP. Individual cases are discussed in some detail, among them norbornenone for which the LC-PBE0 functional produced an optical rotation that is close to available data from coupled-cluster calculations, but significantly smaller in magnitude than the liquid-phase experimental value. Range-separated functionals and BHLYP perform well for helicenes and helicene derivatives. Metal complexes pose a challenge to first-principles calculations of optical rotation.     

Calculation of static and dynamic linear magnetic response in approximate time-dependent density functional theory

We report implementations and results of time-dependent density functional calculations (i) of the frequency-dependent magnetic dipole-magnetic dipole polarizability, (ii) of the (observable) translationally invariant linear magnetic response, and (iii) of a linear intensity differential (LID) which includes the dynamic dipole magnetizability. The density functional calculations utilized density fitting. For achieving gauge-origin independence we have employed time-periodic magnetic-field-dependent basis functions as well as the dipole velocity gauge, and have included explicit density-fit related derivatives of the Coulomb potential. We present the results of calculations of static and dynamic magnetic dipole-magnetic dipole polarizabilities for a set of small molecules, the LID for the SF6 molecule, and dispersion curves for M-hexahelicene of the origin invariant linear magnetic response as well as of three dynamic polarizabilities: magnetic dipole-magnetic dipole, electric dipole-electric dipole, and electric dipole-magnetic dipole. We have also performed comparison of the linear magnetic response and magnetic dipole-magnetic dipole polarizability over a wide range of frequencies for H2O and SF6.     

Resonance Raman scattering of rhodamine 6G as calculated by time-dependent density functional theory: vibronic and solvent effects

The geometries, UV-vis absorption spectra, and resonance Raman (RR) intensities have been determined for the S1 and S3 excited states of rhodamine 6G (R6G) in vacuum and ethanol by means of DFT/TDDFT methodologies with the aim of better understanding the structures and properties of the excited states. The RR spectra have been simulated from the vibronic theory of RR scattering as well as within the short-time approximation, while the solvent effects have been modeled using the polarizable continuum model. The S1 and S3 states of R6G present UV-vis absorption bands with similar vibronic structure, i.e., a shoulder at smaller wavelengths, although this shoulder is relatively more intense and more sensitive to the solvent in the case of S3. These differences are corroborated by the larger geometry relaxations upon excitation for S3 and the fact that the charge transfer of S3 is reduced in ethanol. Moreover, the differences between S1 and S3 are magnified when considering the RR spectra. On one hand, the RR spectrum of R6G in resonance with the S0 --> S1 transition presents many transitions of which the relative intensities strongly vary when the excitation wavelength gets closer to the maximum of absorption. The RR spectrum of R6G in resonance with S1 is however little influenced by the solvent. On the other hand, the RR spectrum of R6G in resonance with the S0 --> S3 transition displays only a few bands, strongly depends on the solvent, and is little affected when changing the excitation wavelength within the limits of the absorption band. As a consequence, the short-time approximation is suitable to reproduce the RR spectrum of R6G in resonance with S3 for a broad range of excitation wavelengths, whereas the vibronic theory approach is needed for describing the RR spectrum of R6G in resonance with S1 close to resonance.     

The adiabatic approximation in time-dependent density matrix functional theory: response properties from dynamics of phase-including natural orbitals

The adiabatic approximation is problematic in time-dependent density matrix functional theory. With pure density matrix functionals (invariant under phase change of the natural orbitals) it leads to lack of response in the occupation numbers, hence wrong frequency dependent responses, in particular α(ω→0)≠α(0) (the static polarizability). We propose to relinquish the requirement that the functional must be a pure one-body reduced density matrix (1RDM) functional, and to introduce additional variables which can be interpreted as phases of the one-particle states of the independent particle reference system formed with the natural orbitals, thus obtaining so-called phase-including natural orbital (PINO) functionals. We also stress the importance of the correct choice of the complex conjugation in the two-electron integrals in the commonly used functionals (they should not be of exchange type). We demonstrate with the Lo?wdin-Shull energy expression for two-electron systems, which is an example of a PINO functional, that for two-electron systems exact responses (polarizabilities, excitation energies) are obtained, while writing this energy expression in the usual way as a 1RDM functional yields erroneous responses.     

Description of core excitations by time-dependent density functional theory with local density approximation, generalized gradient approximation, meta-generalized gradient approximation, and hybrid functionals

Time-dependent density functional theory (TDDFT) is employed to investigate exchange-correlation-functional dependence of the vertical core-excitation energies of several molecules including H, C, N, O, and F atoms. For the local density approximation (LDA), generalized gradient approximation (GGA), and meta-GGA, the calculated X1s-->pi* excitation energies (X = C, N, O, and F) are severely underestimated by more than 13 eV. On the other hand, time-dependent Hartree-Fock (TDHF) overestimates the excitation energies by more than 6 eV. The hybrid functionals perform better than pure TDDFT because HF exchange remedies the underestimation of pure TDDFT. Among these hybrid functionals, the Becke-Half-and-Half-Lee-Yang-Parr (BHHLYP) functional including 50% HF exchange provides the smallest error for core excitations. We have also discovered the systematic trend that the deviations of TDHF and TDDFT with the LDA, GGA, and meta-GGA functionals show a strong atom-dependence. Namely, their deviations become larger for heavier atoms, while the hybrid functionals are significantly less atom-dependent.     

Natural bond orbital analysis, electronic structure, non-linear properties and vibrational spectral analysis of L-histidinium bromide monohydrate: a density functional theory

The spectroscopic properties of the crystallized nonlinear optical molecule L-histidinium bromide monohydrate (abbreviated as L-HBr-mh) have been recorded and analyzed by FT-IR, FT-Raman and UV techniques. The equilibrium geometry, vibrational wavenumbers and the first order hyperpolarizability of the crystal were calculated with the help of density functional theory computations. The optimized geometric bond lengths and bond angles obtained by using DFT (B3LYP/6-311++G(d,p)) show good agreement with the experimental data. The complete assignments of fundamental vibrations were performed on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. The natural bond orbital (NBO) analysis confirms the occurrence of strong intra and intermolecular N-H?O hydrogen bonding.     

Electronic spectrum of UO2(2+) and [UO2Cl4]2- calculated with time-dependent density functional theory

The electronic spectra of UO(2) (2+) and [UO(2)Cl(4)](2-) are calculated with a recently proposed relativistic time-dependent density functional theory method based on the two-component zeroth-order regular approximation for the inclusion of spin-orbit coupling and a noncollinear exchange-correlation functional. All excitations out of the bonding sigma(u) (+) orbital into the nonbonding delta(u) or phi(u) orbitals for UO(2) (2+) and the corresponding excitations for [UO(2)Cl(4)](2-) are considered. Scalar relativistic vertical excitation energies are compared to values from previous calculations with the CASPT2 method. Two-component adiabatic excitation energies, U-O equilibrium distances, and symmetric stretching frequencies are compared to CASPT2 and combined configuration-interaction and spin-orbit coupling results, as well as to experimental data. The composition of the excited states in terms of the spin-orbit free states is analyzed. The results point to a significant effect of the chlorine ligands on the electronic spectrum, thereby confirming the CASPT2 results: The excitation energies are shifted and a different luminescent state is found.     

Accurate evaluation of valence and low-lying Rydberg states with standard time-dependent density functional theory

Using a standard exchange-correlation functional, namely, PBE0, the basis set dependence of time-dependent density functional theory (TD-DFT) calculations has been explored using 33 different bases and five organic molecules as test cases. The results obtained show that this functional can provide accurate (i.e., at convergence) results for both valence and low-lying Rydberg excitations if at least one diffuse function for the heavy atoms is included in the basis set. Furthermore, these results are in fairly good agreement with the experimental data and with those delivered by other functionals specifically designed to yield correct asymptotic/long-range behavior. More generally, the PBE0 calculations show that a greater accuracy can be obtained for both Rydberg and valence excitations if they occur at energies below the epsilonHOMO + 1 eV threshold. This latter value is proposed as a thumb rule to verify the accuracy of TD-DFT/PBE0 applications.     

Theoretical studies on electronic spectroscopy and dynamics with the real-time time-dependent density functional theory

Time-dependent density functional theory (TDDFT) has evolved into a general routine to extract the energies of low-lying excited states over the last decades. Driven by the remarkable progress of laser technology, the study of the interaction between matter and intense laser fields with ultrashort pulse duration develops rapidly. A great number of new strong field phenomena emerge. The requirement of a theoretical tool to study the intense field phenomena and dynamical processes of polyatomic systems is urgent. To extend the power of the TDDFT beyond the linear responses, an alternative scheme has been developed by numerically solving the time-dependent Kohn-Sham equations directly in real-time domain. In this article, we summarize the algorithms and capabilities of the real-time TDDFTon studying electron spectroscopy and dynamics of polyatomic systems. The failure of TDDFT with the adiabatic localdensity approximation on some dynamical processes and the possible solutions are synopsized as well. The numerical implementation of algorithms and applications of RT-TDDFT on the linear and nonlinear spectroscopies and electronic dynamics of nano-size nonmetal clusters are displayed.     

Density matrix based time-dependent density functional theory and the solution of its linear response in real time domain

A density matrix based time-dependent density functional theory is extended in the present work. Chebyshev expansion is introduced to propagate the linear response of the reduced single-electron density matrix upon the application of a time-domain delta-type external potential. The Chebyshev expansion method is more efficient and accurate than the previous fourth-order Runge-Kutta method and removes a numerical divergence problem. The discrete Fourier transformation and filter diagonalization of the first-order dipole moment are implemented to determine the excited state energies. It is found that the filter diagonalization leads to highly accurate values for the excited state energies. Finally, the density matrix based time-dependent density functional is generalized to calculate the energies of singlet-triplet excitations.     

The hydrogen bond in ice probed by soft x-ray spectroscopy and density functional theory

We combine photoelectron and x-ray absorption spectroscopy with density functional theory to derive a molecular orbital picture of the hydrogen bond in ice. We find that the hydrogen bond involves donation and back-donation of charge between the oxygen lone pair and the O-H antibonding orbitals on neighboring molecules. Together with internal s-p rehybridization this minimizes the repulsive charge overlap of the connecting oxygen and hydrogen atoms, which is essential for a strong attractive electrostatic interaction. Our joint experimental and theoretical results demonstrate that an electrostatic model based on only charge induction from the surrounding medium fails to properly describe the internal charge redistributions upon hydrogen bonding.     

Natural bond orbital analysis and density functional study of linear and bent oxo-bridged dimers of rhenium(V)

The calculations using the density functional theory (DFT) method were done on two diamagnetic oxo-bridged dinuclear rhenium complexes: [{Re(O)Br₂(3,5-Me₂pzH)₂}₂(μ-O)] (1) with a linear ORe–O–ReO core and [{Re(O)Br(3,5-Me₂pzH)}₂(μ-O)(μ-3,5-Me₂pz)₂] (2) with a bent Re₂O₃ unit (pzHmonodentate N-pyrazole and pzbidentate N,N′-pyrazole ligand). The optimized geometries of 1 and 2 agree with the X-ray structures. The MO sequence is almost the same for 1 with a linear ORe–O–ReO core and 2 with a bent Re₂O₃ unit. The bending of Re₂O₃ unit in 2 is a consequence of steric congestion introduced by two coordinated 3,5-dimethylopyrazole bridging ligands. Additional information about binding in the complexes 1 and 2 was obtained by NBO analysis.     

Electron-structure calculations and bond order analysis using density functional theory of cationic dinuclear arene ruthenium complexes

The structure and nature of the metal-metal bonding interaction in the cationic complexes [(eta6-C6Me6)2Ru2(mu2-H)3]+ (1), [(eta6-C6Me6)2Ru2(mu2-H)2(mu2-1,4-SC6H4Br)]+ (2), [(eta6-C6Me6)2Ru2(mu2-H)(mu2-1,4-SC6H4Br)2]+ (3), and [(eta6-C6Me6)2Ru2(mu2-1,4-SC6H4Br)3]+ (4) have been studied at the density functional theory (DFT) level using molecular orbital (MO) theory, bond order (BO) analysis, bond decomposition energy (BDE), electron localization function (ELF), and Laplacian of the density methods. The results show that there is no direct bond between the two ruthenium atoms in 1-4, the MO interaction within the diruthenium backbone being stabilized by the bridging ligands. For complex 1, the ELF clearly shows that the bond within the diruthenium backbone is through the three bridging hydride ligands, which act as a sort of glue by forming three-center two-electron bonds characterized by (Ru, H, Ru) basins with 1.8 e mostly located in the H atomic basin.     

In cation interactions with some organics: ab initio molecular orbital and density functional theory

Ab initio molecular orbital and density functional theory studies were undertaken to investigate the structural and energetic characteristics of complexes of In⁺ with several different organic molecules for the first time. HF, MP2, QCISD, and CCD levels of theory in ab initio MO as well as B3LYP, B3PW91 hybrid functionals in density functional theory were used. A valence TZ+P basis set with relativistic effective core potentials was used for the In atom while the 6-311++G(3d, 2p) basis set was utilized for all other atoms. Both closed-shell (H₂O, CH₄, CH₃OH, and C₆H₆) and open-shell (CH₃ and C₂H₃) molecules were considered for complexation with In⁺. In⁺ affinities of 21.5, 24.8, 28.6, 18.4, and 23.0 kcal/mol were obtained with the B3PW91 hybrid functional for H₂O, CH₃OH, C₆H₆, CH₃, and C₂H₃, respectively. The large values for the calculated affinities indicate the validity of our recent experimental detection of In⁺ ion attachment to some organic molecules.