On the calculations of interaction energies and induced electric properties within the polarizable continuum model

In this work we investigate the influence of a polarizable environment on the interaction energies and the interaction-induced (excess) static electric dipole properties for the selected model hydrogen-bonded complexes. The excess properties were estimated for water and hydrogen fluoride dimers using the supermolecular approach and assuming the polarizable continuum model (PCM) as a representation of the polarizable environment. We analyze in this context the performance of the counterpoise correction and the consequences of various possible monomer cavity choices. The polarizable environment reduces the absolute magnitudes of interaction energies and interaction-induced dipole moments, whereas an increase is observed for the absolute magnitudes of induced polarizabilities and first hyperpolarizabilities. Our results indicate that the use of either monomeric (MC) or dimeric (DC) cavities in calculations of monomer properties does not change qualitatively the resultant excess properties. We conclude that the DC scheme is more consistent with the definition of the interaction energy and consequently also the interaction-induced property, whereas the MC scheme corresponds to the definition of stabilization energy. Our results indicate also a good performance of the counterpoise correction scheme for the self-consistent methods in the case of all studied properties.     

Electronic and vibrational contributions to first hyperpolarizability of donor-acceptor-substituted azobenzene

In this study we report on the electronic and vibrational (hyper)polarizabilities of donor-acceptor-substituted azobenzene. It is observed that both electronic and vibrational contributions to the electric dipole first hyperpolarizability of investigated photoactive molecule substantially depend on the conformation. The contributions to the nuclear relaxation first hyperpolarizability are found to be quite important in the case of two considered isomers (cis and trans). Although the double-harmonic term is found to be the largest in terms of magnitude, it is shown that the total value of the nuclear relaxation contribution to vibrational first hyperpolarizability is a result of subtle interplay of higher-order contributions. As a part of the study, we also assess the performance of long-range-corrected density functional theory in determining vibrational contributions to electric dipole (hyper)polarizabilities. In most cases, the applied long-range-corrected exchange-correlation potentials amend the drawbacks of their conventional counterparts.     

Electrostatic calculation of linear and non-linear optical properties of ice Ih,II, IX and VIII

Macroscopic first- and third-order susceptibilities of ice Ih, ice II, ice IX and ice VIII are calculated using static and frequency-dependent electronic and static vibrational molecular (hyper)polarizabilities at the MP2 level. The molecular properties are in good agreement with experiment and with high-level ab initio calculations. Intermolecular electrostatic and polarization effects due to induced dipoles are taken into account using a rigorous local-field theory. The electric field due to permanent dipoles is used to calculate effective in-crystal (hyper)polarizabilities. The polarizability depends only weakly on the permanent field, but the dipole moment and the hyperpolarizabilities are strongly affected. The calculated linear susceptibility is in good agreement with available experimental data for ice Ih, and the third-order susceptibility for a third harmonic generation experiment is in reasonable agreement with experimental values for liquid water. The molecular vibrational contributions have a small effect on the susceptibilities. The electric properties of a water tetramer are calculated and used to estimate the effect of non-dipolar interactions on the susceptibilities of ice Ih, which are found to be small.     

Theory of intermolecular interactions: The long range terms in the dipole–dipole,monopoles–dipole,and monopoles–bond polarizabilities approximations

The problem of evaluating the long range terms (electrostatic, polarization, dispersion) of the interaction energy between molecules at intermediate distances (i.e. distances of the order of magnitude of the molecular dimensions) is considered. Instead of being approximated by its dipole part, the exact interaction Hamiltonian is treated as proposed by Longuet-Higgins [11], i.e. the matrix elements are interpreted as electrostatic interactions between state and transition charge distributions. These charge distributions are approximated in a systematic way by sets of point charges (localized on the atoms) or sets of dipoles (localized on the bonds). The various contributions to the energy may then be expressed in terms of atomic net charges and bond polarizabilities. More refined approximations of the charge distributions could be used and correspondingly improved formulae could be derived: as an example, a formula for the σ-π dispersion energy is derived, where the σ charge distributions are approximated by bond transition dipoles (leading to σ bond polarizabilities in the final formula) while the π charge distributions are approximated by atomic charges.     

Analytic calculation of second-order electric response properties with the normalized elimination of the small component (NESC) method

Analytic second derivatives of the relativistic energy for the calculation of electric response properties are derived utilizing the normalized elimination of the small component (NESC) method. Explicit formulas are given for electric static dipole polarizabilities and infrared intensities by starting at the NESC representation of electric dipole moments. The analytic derivatives are implemented in an existing NESC program and applied to calculate dipole moments, polarizabilities, and the infrared spectra of gold- and mercury-containing molecules as well as some actinide molecules. Comparison with experiment reveals the accuracy of NESC second order electric response properties.     

Quantum-chemical calculation of electrooptical properties of vanillin tautomers

Static dipole polarizabilities and hyperpolarizabilities of benzoid and p-quinoid molecular forms of vanillin were calculated using quantum-chemical method B3LYP/cc-pVTZ. The dominant benzoid tautomers much exceed in hyperpolarizability the m-nitroaniline molecule. Tautomeric transformations and conformational changes significantly affect the vanillin hyperpolarizability. Quinoid tautomers generated by the topochemical reaction of proton transfer between neighboring molecules in a vanillin crystal can promote the second harmonic generation of infrared laser light only as an element of supramolecular nanostructures (linear defects) with a high hyperpolarizability.     

Calculation of the nonlinear optical properties of molecules

A finite-field method for the calculation of polarizabilities and hyperpolarizabilities is developed based on both an energy expansion and a dipole moment expansion. This procedure is implemented in the MOPAC semiempirical program. Values and components of the dipole moment (μ), polarizability (α), first hyperpolarizability (β), and second hyperpolarizability (γ) are calculated as an extension of the usual MOPAC run. Applications to benzene and substituted benzenes are shown as test cases utilizing both MNDO and AM1 Hamiltonians.     

On the vibrational linear and nonlinear optical properties of compounds involving noble gas atoms: HXeOXeH,HXeOXeF, and FXeOXeF

The vibrational (hyper)polarizabilities of some selected Xe derivatives are studied in the context of Bishop–Kirtman perturbation theory (BKPT) and numerical finite field methodology. It was found that for this set of rare gas compounds, the static vibrational properties are quite large, in comparison to the corresponding electronic ones, especially those of the second hyperpolarizability. This also holds for the dc‐Pockels β(?ω;ω,0), Kerr γ(?ω;ω,0,0) and electric field second harmonic generation γ (?2ω;ω,ω,0) effects, although the computed nuclear relaxation (nr) vibrational contributions are smaller in magnitude than the static ones. HXeOXeH was used to study the effects of electron correlation, basis set, and geometry. Geometry effects were found to lead to noticeable changes of the vibrational and electronic second hyperpolarizability. A limited study of the effect of Xe insertion to the nr vibrational properties is also reported. Assessment of the results revealed that Xe insertion has a remarkable effect on the nr (hyper)polarizabilities. In terms of the BKPT, this is associated with a remarkable increase of the electrical and mechanical anharmonicity terms. The latter is consistent with the anharmonic character of several vibrational modes reported for rare gas compounds. © 2013 Wiley Periodicals, Inc.     

Amine-hydrogen halide complexes: experimental electric dipole moments and a theoretical decomposition of dipole moments and binding energies

The Stark effect has been observed in the rotational spectra of several gas-phase amine-hydrogen halide complexes and the following electric dipole moments have been determined: H(3)(15)N-H(35)Cl (4.05865 +/- 0.00095 D), (CH(3))(3)(15)N-H(35)Cl (7.128 +/- 0.012 D), H(3)(15)N-H(79)Br (4.2577 +/- 0.0022 D), and (CH(3))(3)(15)N-H(79)Br (8.397 +/- 0.014 D). Calculations of the binding energies and electric dipole moments for the full set of complexes R(n)()(CH(3))(3)(-)(n)()N-HX (n = 0-3; X = F, Cl, Br) at the MP2/aug-cc-pVDZ level are also reported. The block localized wave function (BLW) energy decomposition method has been used to partition the binding energies into contributions from electrostatic, exchange, distortion, polarization, and charge-transfer terms. Similarly, the calculated dipole moments have been decomposed into distortion, polarization, and charge-transfer components. The complexes studied range from hydrogen-bonded systems to proton-transferred ion pairs, and the total interaction energies vary from 7 to 17 kcal/mol across the series. The individual energy components show a much wider variation than this, but cancellation of terms accounts for the relatively narrow range of net binding energies. For both the hydrogen-bonded complexes and the proton-transferred ion pairs, the electrostatic and exchange terms have magnitudes that increase with the degree of proton transfer but are of opposite sign, leaving most of the net stabilization to arise from polarization and charge transfer. In all of the systems studied, the polarization terms contribute the most to the induced dipole moment, followed by smaller but still significant contributions from charge transfer. A significant contribution to the induced moment of the ion pairs also arises from distortion of the HX monomer.     

Electronic structure, bonding, spectra, and linear and nonlinear electric properties of Ti@C28

The potential energy surface (PES) of Ti@C(28) has been revisited, and the stationary points have been carefully characterized. In particular, the C(2v) symmetry structure considered previously turns out to be a transition state lying 2.3 kcal/mol above the ground state of C(3v) symmetry at the MP2/6-31G(d) level. A large binding energy of 181.3 kcal/mol is found at the ROMP2/6-31G(d) level. Topological analysis of the generalized Ti@C(28) density reveals four bond paths between Ti and carbon atoms of the host. The character of all four contacts corresponds to a partially covalent closed shell interaction. UV-vis, IR, and Raman spectra are calculated and compared with C(28)H(4). The dipole moment and the static electronic and double harmonic vibrational (hyper)polarizabilities have been obtained. Distortion of the fullerene cage due to encapsulation leads to nonzero diagonal components of the electronic first hyperpolarizability β, and to an increase in the diagonal components of the electronic polarizability α and second hyperpolarizability γ. However, introduction of the Ti atom causes a comparable or larger reduction in most cases due to localized bonding interactions. At the double harmonic level, the average vibrational β is much larger than its electronic counterpart, but the opposite is true for α and for the contribution to γ that has been calculated. There is also a very large anharmonic (nuclear relaxation) contribution to β which results from a shallow PES with four minima separated by very low barriers. Thus, the vibrational γ (and α) may, likewise, become much larger when anharmonicity is taken into account.     

A bilayer model of the double hysteresis loop in antiferroelectric liquid crystals

We investigate, both analytically and numerically, a simple model of the field induced double hysteresis loop in AFLC materials. This bilayer model of the bulk of an AFLC describes the free energy in terms of polar and non-polar interactions due to surface alignment, the electric field/dipole interaction in each layer and the dipole/dipole interaction between the layers. The static hysteresis loop is found analytically and the stability of each analytic solution is investigated. The dynamic switching characteristics are found numerically and then investigated as the system parameters and electric field characteristics are changed.     

Accuracy of distributed multipoles and polarizabilities: comparison between the LoProp and MpProp models

Localized multipole moments up to the fifth moment as well as localized dipole polarizabilities are calculated with the MpProp and the newly developed LoProp methods for a total of 20 molecules, predominantly derived from amino acids. A comparison of electrostatic potentials calculated from the multipole expansion obtained by the two methods with ab initio results shows that both methods reproduce the electrostatic interaction with an elementary charge with a mean absolute error of approximately 1.5 kJ/mol at contact distance and less than 0.1 kJ/mol at distances 2 A further out when terms up to the octupole moments are included. The polarizabilities are tested with homogenous electric fields and are found to have similar accuracy. The MpProp method gives better multipole moments unless diffuse basis sets are used, whereas LoProp gives better polarizabilities.     

Dipole Cauchy moments of the atoms H through Ar

Summary Dipole Cauchy moments of the atoms through Ar are calculated using the hydrodynamic formulation of time-dependent Kohn-Sham theory. The exchange-correlation energy density functional is approximated by the gradient expansion for atoms. Using variational trial functions that contain both linear and nonlinear variational parameters, we are able to reproduce (to three or four significant figures) the static dipole polarizabilities obtained by explicitly solving the relevant differential equations. The resulting dipole Cauchy moments provide a convenient starting point for calculating other properties which result from the linear interaction of atoms with a time varying electric field.     

Vibrational contributions to static linear and nonlinear optical coefficients: from two-level to two-band systems

The importance of vibrational contributions to the static linear and nonlinear optical coefficients is investigated. We apply the exact sum-over-state (SOS) formulas for polarizabilities and hyperpolarizabilities expressed in terms of vibronic states to a two-level system with a single vibrational mode. The Herzberg–Teller expansion is applied to the SOS formulas including vibrational energy levels without employing the Placzek’s approximation within both the Born–Oppenheimer approximation and electrical and mechanical harmonicities. The results include not only the vibrational contribution from the lattice relaxation expression but also the contribution arising from the higher-order correction terms. Model calculations on a diatomic system with two electronic states show that the contribution of these correction terms is small. Moreover, most of these higher-order terms are negligible in the solid-state limit. In polyacetylene, the contribution of the lattice relaxation expression is much larger than that in the diatomic case. Within the tight-binding approximation, the contribution of the lattice relaxation expression is 44% of the pure electronic contribution for the second hyperpolarizability.     

Calculations of static dipole polarizabilities of alkali dimers: prospects for alignment of ultracold molecules

The rapid development of experimental techniques to produce ultracold alkali molecules opens the ways to manipulate them and to control their dynamics using external electric fields. A prerequisite quantity for such studies is the knowledge of their static dipole polarizability. In this paper, we computed the variations with internuclear distance and with vibrational index of the static dipole polarizability components of all homonuclear alkali dimers including Fr(2), and of all heteronuclear alkali dimers involving Li to Cs, in their electronic ground state and in their lowest triplet state. We use the same quantum chemistry approach as in our work on dipole moments [Aymar and Dulieu, J. Chem. Phys. 122, 204302 (2005)], based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective potentials for core polarization. Polarizabilities are extracted from electronic energies using the finite-field method. For the heaviest species Rb(2), Cs(2), and Fr(2) and for all heteronuclear alkali dimers, such results are presented for the first time. The accuracy of our results on atomic and molecular static dipole polarizabilities is discussed by comparing our values with the few available experimental data and elaborate calculations. We found that for all alkali pairs, the parallel and perpendicular components of the ground state polarizabilities at the equilibrium distance R(e) scale as (R(e))(3), which can be related to a simple electrostatic model of an ellipsoidal charge distribution. Prospects for possible alignment and orientation effects with these molecules in forthcoming experiments are discussed.     

Gaussian induced dipole polarization model

A new induced dipole polarization model based on interacting Gaussian charge densities is presented. In contrast to the original induced point dipole model, the Gaussian polarization model is capable of finite interactions at short distances. Aspects of convergence related to the Gaussian model will be explored. The Gaussian polarization model is compared with the damped Thole-induced dipole model and the point dipole model. It will be shown that the Gaussian polarization model performs slightly better than the Thole model in terms of fitting to molecular polarizability tensors. An advantage of the model based on Gaussian charge distribution is that it can be easily generalized to other multipole moments and provide effective damping for both permanent electrostatic and polarization models. Finally, a method of parameterizing polarizabilities is presented. This method is based on probing a molecule with point charges and fitting polarizabilities to electrostatic potential. In contrast to the generic atom type polarizabilities fit to molecular polarizability tensors, probed polarizabilities are significantly more accurate in terms of reproducing molecular polarizability tensors and electrostatic potential, while retaining conformational transferability.     

DFT calculations of static dipole polarizabilities and hyperpolarizabilities for the boron clusters Bn (n=3–8,10)

The static electric dipole polarizabilities and second‐order hyperpolarizabilities of several bare boron clusters have been calculated with density functional theory. The average second‐order hyperpolarizability γ_av reaches a saturation limit of about 50,000 a.u. already with B₅ for a given type of structure. The average polarizability per atom shows overall a decrease with increasing cluster size, while the average second hyperpolarizability per atom first increases from B₃ to B₆, and then starts to decrease. For the noncentrosymmetric clusters dipole moments and first‐order hyperpolarizabilities are reported. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 131–135, 2000     

Direct metal-metal interaction contributions to quadratic hyperpolarizability: a study on dirhenium complexes

We present a comparative study of the metal-metal interaction effect on the static quadratic hyperpolarizabilities of two typical dinuclear rhenium clusters. The electronic structures, excitation spectra, dipolar moments, static polarizabilities, and quadratic hyperpolarizabilities of the two complexes with direct metal-metal interactions have been computed and analyzed with the use of high-level DFT/TDDFT methods. The geometries and the first intense excitations agree with the relevant reported measurements. The orbital decomposition scheme ( J. Phys. Chem. A 2006, 110, 1014-1021) has been applied to analyze the relationship between the electronic structures and nonlinear optical (NLO) properties of these two complexes. We propose an unprecedented NLO response mechanism featuring the contribution of the direct metal-metal interaction transition process in these dinuclear rhenium complexes. This contribution positively enhances the quadratic hyperpolarizability and relates to the intensity of the metal-metal interactions of the complexes. The results are helpful to the development of NLO chromophores in polynuclear metal clusters through the molecular design technique.     

Nonlinear optical properties of carbon nitride nanotubes

The second order polarizabilities (β) of the C(3)N(4) NT systems were investigated in this study. The β values of end groups substituted C(3)N(4) NTs were calculated to find their most favorable paradigm for nonlinear optical design. It was found that their electric dipole transitions are only allowed along the tube axis direction and the position of terminal groups has a great effect on NLO properties of substituted C(3)N(4) NTs. The obtained results provide us details to understand the relation between the structure and nonlinear optical properties. The results indicate that the second-order polarizabilities originate from charge transfer from a donor (-NH(2)) to an acceptor (-O(2)N) and the electron density redistribution in heptazine units. We employ a one-dimensional two-state model to analyze the nature of the second-order polarizabilities of studied materials. The frequency-dependent second-order polarizabilities were also calculated. The second-order polarizability of the O(2)N-C(3)N(4)-NH(2) NT is 2.51 × 10(-27) esu when the input photon energy is 2.232 eV, which is much larger (about two orders of magnitude) than static second-order polarizability (2.54 × 10(-29)).