Calculation of origin-independent optical rotation tensor components in approximate time-dependent density functional theory

We outline an implementation of the origin-independent optical rotation tensor, which includes electric dipole-magnetic dipole and electric dipole-electric quadrupole polarizability. The method is based on approximate time-dependent density functional theory. We utilize time-periodic magnetic-field-dependent basis functions as well as a modified velocity-gauge formulation of dynamic polarizability tensors in order to obtain a gauge-origin independence. To ensure gauge-origin independence of the results within a given numerical accuracy, density fit coefficient derivatives are employed. A damping constant has been introduced into the linear response equations to treat both resonance and nonresonance regions of optical activity. We present calculations for trans-2,3-dimethyloxirane and derivatives thereof as well as calculations for androst-4,17-dien-3-one. In the Appendix, we derive the equivalence between the common-gauge origin and gauge-including atomic orbitals formulations for the optical rotation tensor in time-dependent DFT.     

The angular dependence of the multipole–multipole interaction for energy transfer

The interaction between multipoles is not isotropic even in cubic systems. This results in the introduction of geometric reduction factors in the calculation of energy-transfer rates in crystals. We derive these reduction factors for the cases of dipole–dipole, dipole–quadrupole, and quadrupole–quadrupole couplings and present a general procedure for their derivation in other cases. For the dipole–dipole case the geometric factor is independent of the distribution of the acceptor species, but for higher-order couplings, a significant angular dependence is found. Received: 6 November 1998 / Accepted: 15 January 1999 / Published online: 7 June 1999     

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.     

A density functional theory test study on the N2··· He dimer

 In the present contribution we report a study of the weakly bound van der Waals N₂–He molecule in the framework of the supermolecule approach by means of the PWPW and mPW1PW exchange–correlation functionals, using density functional theory local-spin-optimized atom-centered basis sets complemented with bond functions optimized at the mPW1PW level of theory. Calculations show that the mPW1PW functional using bond functions gives a realistic representation of the interaction-energy potentials for this van der Waals dimer, comparable to reference M?ller–Plesset perturbation theory calculations. In contrast, the PWPW functional is unable to describe the bonding properties of this system and all values of the bonding properties obtained at different geometries with this functional are considered out-of-scale compared with the rest of the calculations presented in this study. Received: 30 October 2000 / Accepted: 3 January 2001 / Published online: 3 April 2001     

Molecular geometry and polarizability of small cadmium selenide clusters from all-electron ab initio and Density Functional Theory calculations

We have calculated molecular geometries and electric polarizabilities for small cadmium selenide clusters. Our calculations were performed with conventional ab initio and density functional theory methods and Gaussian-type basis sets especially designed for (CdSe)(n). We find that the dipole polarizability per atom converges rapidly to the bulk value.     

Geometry, dipole moment, polarizability and first hyperpolarizability of polymethineimine: an assessment of electron correlation contributions

We have investigated the geometries as well as the longitudinal dipole moment (micro), polarizability (alpha), and first hyperpolarizability (beta) of polymethineimine oligomers using different approaches [Hartree-Fock (HF), second-order M?ller-Plesset (MP2), and hybrid density functional theory (DFT) methods (B3LYP and PBE0)] for evaluating the geometries and the nonlinear optical properties. It turns out that (i) HF and the selected DFT methods provide the incorrect sign for beta of short and medium size oligomers. (ii) The B3LYP and PBE0 electron correlation correction are too small for micro, too large for alpha, and for some oligomer lengths, they are in the wrong direction for beta. (iii) On the contrary to polyacetylene, the hybrid-DFT geometries are in poor agreement with MP2 geometries; the former showing much smaller bond length alternations.     

Calculation of the electric susceptibilities of the helium atom

We calculated the static and the dynamic dipole polarizabilities and the static quadrupole polarizability of the helium atom. The results are α = 0.2070 × 10^?24 cm³ for the static dipole polarizability and γ₄ = 0.1038 × 10^?40 cm⁵ for the static quadrupole polarizability.     

Electric properties of hydrogen iodide: Reexamination of correlation and relativistic effects

The electric dipole moment and the static dipole polarizability of the hydrogen iodide molecule were studied using sophisticated correlated and relativistic methods. Both scalar and spin–orbit relativistic effects were carefully accounted for. We conclude that the large differences between the theoretical and experimental dipole moment, the dipole moment derivative and the polarizability cannot be reconciled by improved account of electron correlation and relativistic effects. The most striking difference between theory and experiment is observed for the polarizability anisotropy. We believe that experimental data, namely the experimental dipole moment (the most recent value is 0.176 au as compared to our best theoretical estimate, 0.154±0.003 au), the parallel polarizability (44.4 and 38.47±0.05 au) and the anisotropy (11.4 and 2.33±0.05 au) must be inaccurate. Experimental and theoretical perpendicular polarizability components (33.0 and 36.14±0.05 au,) and the mean polarizability (36.8 and 36.92±0.05 au) agree better. Our vibrationally corrected relativistic CCSD(T) results represent the most sophisticated predictions of electric properties of HI obtained so far.Contribution to the Björn Roos Honorary Issue     

trans-1,2-Dicyano-cyclopropane and other cyano-cyclopropane derivatives

In this work we present the experimental vibrational absorption (VA), vibrational circular dichroism (VCD) and Raman spectra for (+)-trans-1(S),2(S)-dicyanocyclopropane and its dideuterio derivative, trans-1(S),2(S)-dicyano-1(S),2(S)-dideuteriocyclopropane, along with VA, VCD, Raman and Raman optical activity (ROA) spectral simulations. Here we investigate the applicability of various local and non-local exchange-correlation (XC) functionals, hybrids and meta-hybrids to reproduce the vibrational spectra of this strained ring system, which also bears two cyano groups. At the highest level of theory, B3PW91/ aug-cc-pVTZ, we also investigated the trans-, cis- and gem-dicyanocyclopropane (trans-, cis-, and gem-DCCP), cyanocyclopropane (CCP) and the parent molecule cyclopropane (CP). In doing so we have investigated the electronic effects (coupling) between the cyano groups and the cyclopropane ring. In addition to providing an interpretation of the experimentally observed vibrational spectra for these molecules, this work also provides benchmark calculations for other methods, especially semi-empirical based wave function and density functional theory (DFT) based methods, such as SCC-DFTB and PM6. For the semi-empirical DFT based methods to be used for 3-membered ring systems, one ought to document their reliability for systems which were not used in the parameterization. The small 3- and 4-membered ring systems are good test systems because they contain non-standard bonding, which may be difficult to determine accurately with the approximations used in the SCC-DFTB and other semi-empirical methods. Like molecular mechanics force fields, semi-empirical methods, based on DFT and wave function quantum mechanics (WFQM), must be benchmarked against high level ab initio and DFT calculations and experimental data. In addition to bonding, the changes in the electric dipole moment, magnetic dipole moment, electric dipole-electric dipole polarizability, electric dipole-magnetic dipole polarizability and electric dipole-electric quadrupole polarizability with respect to nuclear displacement and nuclear velocity can be determined by the VA, VCD, Raman and ROA intensities. Hence it is important that the semi-empirical based DFT and wave function methods not only be parameterized to determine energies, gradients and Hessians, but also the electric and magnetic moments and their derivatives that determine the electronic and magnetic properties of these molecules and their interactions with matter and radiation. This will allow biochemists, biophysicists, molecular biologists, and physical biologists to use experimental and theoretical VA, VCD, Raman and ROA spectroscopies to probe biophysical and biochemical function and processes at the molecular level. Festschrift in Honor of Philip J. Stephens’ 65th Birthday.     

Assessment of the Van Voorhis–Scuseria exchange–correlation functional for predicting excitation energies using time-dependent density functional theory

We assess the performance of the Van Voorhis–Scuseria exchange–correlation functional (VSXC), a kinetic-energy-density-dependent exchange–correlation functional recently developed in our group, for calculating vertical excitation energies using time-dependent density functional theory in a benchmark set of molecules. Overall, VSXC performs very well, with accuracy similar to that of hybrid functionals such as the hybrid Perdew–Burke–Ernzerhof functional and Becke's three parameter hybrid method with the Lee, Yang, and Parr correlation functional, which contain a portion of Hartree–Fock exchange. Received: 29 December 1999 / Accepted: 5 June 2000 / Published online: 11 September 2000     

Polarizabilities of heteroaromatic molecules: Azines revisited

Ab initio electron-correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities are reported for benzene and 12 heteroaromatic six-membered rings obtained from it by aza-substitution. Our geometries and dipole moments agree well with available experimental microwave determinations. The polarizabilities are in reasonable agreement with the fragmentary experimental data available. Uncoupled Hartree-Fock calculations indicate that as much as half the polarizability comes from the σ-electrons. Simple empirical formulas based on atom- and bond-additive models correlate the calculated polarizabilities of 33 five- and six-membered heteroaromatic rings (10 azoles, 10 oxazoles, 13 azines) quite well. The correlation improves significantly if systematic data of uniform quality are used. © 1996 John Wiley & Sons, Inc.     

Evaluation of the 1-octanol/water partition coefficient of nucleoside analogs via free energy estimated in quantum chemical calculations

The partition coefficients (logP) of nucleoside analogs determined by the difference in the free energies of hydration and solvation in water-saturated octanol using the thermodynamic integration method are reported. The logP values calculated in this approach are closer to the experimental values compared to other ab initio methods. Solvation free energy in water and octanol, free energy of cavity formation in water and Henry’s constants, and some other parameters are estimated at the density functional theory (DFT) and Hartree-Fock level with 6–31G*, 6–31G, and 6–31+G basis sets. Surface area, mass, refractivity, volume, polarizability, and dipole moment are calculated for some drugs with HF and DFT methods. The results show that log P decreases with the decrease in polarizability and the increase in dipole moment.     

Some thoughts about the stability and reliability of commonly used exchange–correlation functionals – coverage of dynamic and nondynamic correlation effects

 The self-interaction error (SIE) of commonly used density functional theory (DFT) exchange functionals mimics long-range (nondynamic) pair correlation effects in an unspecified way. Slater exchange suffers from a larger SIE and, therefore, covers more nondynamic correlation effects than Becke exchange, which is the reason why exchange–correlation (XC) functionals based on Slater exchange lead to stabler restricted DFT solutions than those based on Becke exchange. However, the stability of an XC functional does not guarantee higher accuracy. On the contrary, if system-specific nondynamic correlation effects have to be introduced via the form of the wave function, these will be suppressed by nondynamic correlation effects already covered by the exchange functional. Hybrid functionals suffer less from the SIE and, therefore, cover a smaller number of nondynamic electron correlation effects. Accordingly, they are better suited when nondynamic electron correlation has to be introduced by the form of the wave function. It is shown that, for example, broken-symmetry unrestricted DFT calculations are more accurate when carried out with B3LYP than BLYP contrary to claims made in the literature. Received: 8 November 2001 / Accepted: 30 January 2002 / Published online: 8 April 2002     

Structures and excitation energies of Zn–tetraarylporphyrin analogues: A theoretical study

The photophysical properties of β-substituted Zn–tetraarylporphyrin (ZnTAP) analogues used as dyes in dye-sensitized solar cells were studied using density functional theory (DFT). Singlet-excitation energy calculations of ZnTAP analogues were performed using time-dependent DFT with B3LYP, B3PW91, PBE0 exchange–correlation functionals at 6-31G(d) and 6-31+G(d) basis sets using B3LYP/6-31G(d) geometries. The PBE0 functional at 6-31+G(d) basis set provided a better correlation with the experimental data for both B- and Q-bands. The inclusion of solvation effect in the calculations provided a good agreement in terms of B:Q_ave ratio of the oscillator strengths for both analogues with the experimental values. Analogue 2 has a higher and a more balanced charge-carrier transport rates than analogue 1. In general, the addition of an electron-donating group in the meso-substituent (analogue 2) resulted in a narrower band gap, higher oscillator strength, a more red-shifted absorption spectra, and better charge-transfer characteristics than analogue 1.     

Ab initio and DFT study of the geometric structures and static dipole (hyper)polarizabilities of aromatic anions

The geometries and the static dipole (hyper)polarizabilities (alpha, beta, gamma) of a series of aromatic anions were investigated at the ab initio (HF, MP2, and MP4) and density functional theory DFT (B3LYP) levels of theory. The anions chosen for the present study are the benzenethiolate (Ph-S-), benzenecarboxylate (Ph-CO2-), benzenesulfinate (Ph-SO2-), benzenesulfonate (Ph-SO3-), and 1,3-benzenedicarboxylate (1,3-Ph-(CO2)2(2-)). For benzenethiolate anion, additional alpha, beta, and gamma calculations were performed at the coupled cluster CCSD level with MP2 optimized geometries. The standard diffuse and polarized 6-31+G(d,p) basis set was employed in conjunction to the ab initio and DFT methods. Additional HF calculations were performed with the 6-311++G(3d,3p) basis set for all the anions. The correlated electric properties were evaluated numerically within the formalism of finite field. The optimized geometries were analyzed in terms of the few reports about the phenolate and sulfonate ions. The results show that electron correlation effects on the polarizabilities are very important in all the anion series. Was found that Ph-SO2- is highly polarizable in terms of alpha and beta, and the Ph-S- is the highest second hyperpolarizable in the series. The results of alpha were rationalized in terms of the analysis of the polarization of charge based in Mulliken atomic population and the structural features of the optimized geometries of anions, whereas the large differences in the beta and gamma values in the series were respectively interpreted in terms of the bond length alternation BLA and the separation of charge in the aromatic ring by effects of the substitution. These results allowed us to suggest the benzenesulfinate and benzenethiolate anions as promising candidates that should be incorporated in ionic materials for second and third-order nonlinear optical devices.     

Theoretical study of a conjugated aromatic molecular wire

In this study, an organic conjugated molecule, 4,4′-[ethane-1,2-diylidenedi(nitrilo)] dibenzenthiol designed and is proposed as a molecular wire. Structural and electronic responses of this aromatic molecular wire to the static electric field with intensities −1.6 × 10⁻² to +1.6 × 10⁻² a.u., are studied using the DFT-B3LYP/6-31G* level of theory. Natural bond orbital atomic charge analysis shows that the imposition of static external electric field induces polarization—localization of charge on the two ends of molecule, especially on considered terminal contact sulfur atoms. The frontier molecular orbitals (MOs) energy levels including the highest occupied MO (HOMO) and the lowest unoccupied MO (LUMO) and the HOMO–LUMO gap (HLG) values are modified by the static electric field as well. The electric dipole moment and polarizability of the proposed molecular wire under the studied electric field strengths are considerably increased. The current–voltage characteristic curve is estimated for the proposed molecular wire.     

Accurate theoretical IR and Raman spectrum of Al2O2 and Al2O3 molecules

The accurate harmonic vibration frequencies together with the infrared (IR) and Raman intensities of the most stable conformers of Al₂O₂ and Al₂O₃ molecules have been calculated by the density functional theory (DFT) method with B3LYP exchange–correlation potential and using a set of the augmented correlated consistent basis sets up to quintuple order. The anharmonic vibration frequencies of the non-linear Al₂O₂ molecule have also been calculated. The obtained equilibrium geometrical parameters, harmonic and anharmonic vibration frequencies along with the IR and Raman intensities good converge to their limits with increasing the size of the used basis set. A comparison of the calculated harmonic and anharmonic vibrational frequencies with the available experimental ones points out that the small differences between the calculated harmonic and experimental frequencies can be further substantially reduced when calculations of the anharmonic vibrational frequencies will be available for all types of molecular geometries.