Static and dynamic second hyperpolarizability calculated by time-dependent density functional cubic response theory with local contribution and natural bond orbital analysis

The static and dynamic second hyperpolarizability gamma has been investigated by time-dependent density functional cubic response theory. The third-order coupled perturbed Kohn-Sham equations were solved to obtain the third-order perturbed charge density. Calculations on a number of small molecules (N(2), CO(2), C(2)H(4), CO, HF, H(2)O, and CH(4)), paradisubstituted oligoacetylene chains, benzene, and eight paradisubstituted benzenes were performed to verify the implementation and to assess the accuracy of the nonhybrid and hybrid time-dependent density functional theory computations. Nitroaniline and a derivative were taken as examples to investigate the distribution of the "gamma density" and to demonstrate the feasibility of analyzing cubic response functions in terms of contributions from natural bond orbitals (NBOs) and natural localized molecular orbitals (NLMOs). The results highlight the contributions from atoms and bonds on different functional groups to the total value of gamma based on the NBO/NLMO analysis, which might be helpful for new nonlinear optical materials design.     

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.     

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.     

Sensitivity analysis and uncertainty calculation for dispersion corrected density functional theory

The precision of binding energies and distances computed with dispersion-corrected density functional theory (DFT-D) is investigated by propagation of uncertainties, yielding relative uncertainties of several percent. Sensitivity analysis is used to calculate the geometry-dependent relative importance of each input parameter for the dispersion correction. While DFT-Ds are exact at asymptotically large distances, their damping functions are shown to play a significant role in binding geometries. This is demonstrated in detail for the interlayer binding of graphite. The techniques presented allow practitioners to quickly compute error bars and to get an a posteriori estimate about the transferability of their results. They can also aid the development of future dispersion corrections.     

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.     

Theoretical investigation on electronic structure and stability of some inverted cucurbiturils by density functional theory

Structure and stability of diastereoisomers of cucurbit[n]urils (CB[n = 5–10]), the inverted CB[n]s, were investigated by density functional theory (DFT) computations. All the inverted CB[n]s were less stable than their normal CB[n]s and the mono-inverted ones with one inverted glycoluril unit in their structures were more stable than their doubly-inverted isomers. Relative change in dipole moments and molecular electrostatic potentials (MEP) were discussed with the deformation in geometric structure and charge distribution of the normal and inverted CB[n]s.     

Regional self-interaction correction of density functional theory

We propose a new simple scheme for self-interaction correction (SIC) of exchange functionals in the density functional theory. In the new scheme, exchange energies are corrected by substituting exchange self-interactions for exchange functionals in regions of self-interaction. To classify the regions of self-interaction, we take advantage of the property of the total kinetic energy density approaching the Weizs?cker density in the case of electrons in isolated orbitals. The scheme differs from conventional SIC methods in that it produces optimized molecular structures. Applying the scheme to the calculation of reaction energy barriers showed that it provides a clear improvement in cases where the barriers are underestimated by conventional "pure" functionals. In particular, we found that this scheme even reproduces a transition state that is not given by pure functionals.     

A localized orbital analysis of the thermochemical errors in hybrid density functional theory: achieving chemical accuracy via a simple empirical correction scheme

This paper describes an empirical localized orbital correction model which improves the accuracy of density functional theory (DFT) methods for the prediction of thermochemical properties for molecules of first and second row elements. The B3LYP localized orbital correction version of the model improves B3LYP DFT atomization energy calculations on the G3 data set of 222 molecules from a mean absolute deviation (MAD) from experiment of 4.8 to 0.8 kcal/mol. The almost complete elimination of large outliers and the substantial reduction in MAD yield overall results comparable to the G3 wave-function-based method; furthermore, the new model has zero additional computational cost beyond standard DFT calculations. The following four classes of correction parameters are applied to a molecule based on standard valence bond assignments: corrections to atoms, corrections to individual bonds, corrections for neighboring bonds of a given bond, and radical environmental corrections. Although the model is heuristic and is based on a 22 parameter multiple linear regression to experimental errors, each of the parameters is justified on physical grounds, and each provides insight into the fundamental limitations of DFT, most importantly the failure of current DFT methods to accurately account for nondynamical electron correlation.     

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.     

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.     

Linearity condition for orbital energies in density functional theory: construction of orbital-specific hybrid functional

This study proposes a novel approach to construct the orbital-specific (OS) hybrid exchange-correlation functional by imposing the linearity condition: ?(2)E/?f(i)(2)|(0≤f(i)≤1) = ??(i)/?f(i)|(0≤f(i)≤1) = 0, where E, ε(i), and f(i) represent the total energy, orbital energy, and occupation number of the ith orbital. The OS hybrid exchange-correlation functional, of which the OS Hartree-Fock exchange (HFx) portion is determined by the linearity condition, reasonably reproduces the ionization potentials not only from valence orbitals but also from core ones in a sense of Koopmans' theorem. The obtained short-range HFx portions are consistent with the parameters empirically determined in core-valence-Rydberg-Becke-3-parameter-Lee-Yang-Parr hybrid functional [Nakata et al., J. Chem. Phys., 124, 094105 (2006); ibid, 125, 064109 (2006)].     

Conformational aspects of glutathione tripeptide: electron density topological & natural bond orbital analyses

Glutathione tripeptide (γ-glutamyl-cysteinyl-glycine) is a flexible molecule and its conformational energy landscape is strongly influenced by forming intramolecular hydrogen bond, its charge and the environment. This study employs DFT-B3LYP method with the 6-31+G (d,p) basis set to carry out conformational analysis of neutral, zwitterionic, cationic, and anionic forms of glutathione. In analyzing the structural characteristics of these structures, intramolecular hydrogen bonds were identified and characterized in details by topological parameters such as electron density ρ(r) and Laplacian of electron density $ \nabla^{2} $ ρ(r) from Bader’s atom in molecules theory. Charge transfer energies based on natural bond orbital analysis are also considered to interpret these intramolecular hydrogen bonds. Our results show that these hydrogen bonds are partially electrostatic and partially covalent in nature, in which the covalent contribution increases as the stabilization energy of hydrogen bond increases. Furthermore, the back bone and side chain (Ramachandran map) orientations of various ionic forms of glutathione have been studied and conformation of each constitution of glutathione tripeptide (i.e., Glu, Cys, and Gly moieties) was determined. In most species side chain conformation were found to be hindered gauche–gauche orientation by intramolecular hydrogen bonds.     

Photoisomerization of stilbene: a spin-flip density functional theory approach

The photoisomerization process of 1,2-diphenylethylene (stilbene) is investigated using the spin-flip density functional theory (SFDFT), which has recently been shown to be a promising approach for locating conical intersection (CI) points (Minezawa, N.; Gordon, M. S. J. Phys. Chem. A2009, 113, 12749). The SFDFT method gives valuable insight into twisted stilbene to which the linear response time-dependent DFT approach cannot be applied. In contrast to the previous SFDFT study of ethylene, a distinct twisted minimum is found for stilbene. The optimized structure has a sizable pyramidalization angle and strong ionic character, indicating that a purely twisted geometry is not a true minimum. In addition, the SFDFT approach can successfully locate two CI points: the twisted-pyramidalized CI that is similar to the ethylene counterpart and another CI that possibly lies on the cyclization pathway of cis-stilbene. The mechanisms of the cis--trans isomerization reaction are discussed on the basis of the two-dimensional potential energy surface along the twisting and pyramidalization angles.     

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.     

Ground-state properties of benzenoid hydrocarbons by simple bond orbital resonance theory approach

π-electron energies and bond orders of benzenoid hydrocarbons with up to five fused hexagons have been considered by the simple Bond Orbital Resonance Theory (BORT) approach. The corresponding ground states were determined according to four BORT models. In the first three models a diagonalisation of the Hückel-type Hamiltonian was performed in the bases of Kekulé, of Kekulé and mono-Claus and of Kekulé and Claus resonance structures, respectively. In the fourth model a simple BORT ansatz was used. According to this ansatz, the ground state is a linear combination of the positive Kekulé structures, all with equal coefficients. It was shown that π-electron energies and bond orders obtained by these models correlate much better with the PPP energies and bond orders than with the Hückel energies and bond orders. This indicates that a simple BORT approach is quite reliable in predicting the more sophisticated PPP results. Concerning the relative performance of the four BORT models, the best results were obtained with the BORT ansatz. The performance deteriorates with the expansion of the basis set. This is attributed to the fact that in these models the improvement of the basis set is not accompanied with the corresponding improvement of the Hamiltonian. Comparing the BORT-ansatz bond orders with the Pauling bond orders, it was shown that BORT-ansatz bond orders correlate much better with the PPP bond orders. This revised version was published online in July 2006 with corrections to the Cover Date.