Vibrational corrections to electric properties of weakly bound systems

The pure electronic and vibrational contributions to electric dipole moments, dipole polarizabilities, and first hyperpolarizabilities have been evaluated for the HF and H₂O dimers. The zero-point vibrational average corrections to dipole moments and dipole polarizabilities turn out to be relatively small. However, the corresponding contributions to the first hyperpolarizability are found to be of the same magnitude as the pure electronic values. The so-called pure vibrational corrections to the dipole polarizability and first hyperpolarizability of hydrogen bonded dimers are exceptionally large and indicate that the perturbation theory method used for their evaluation fails to account properly for the high mechanical and electric anharmonicities present in these systems. The analysis of different harmonic and anharmonic contributions to the pure vibrational correction to the first hyperpolarizability shows explicitly the importance of the low frequency intermolecular modes.     

Calculations of the polarizability and hyperpolarizability of the NaH molecule including vibrational corrections

In this work we present results for the dipole moment, polarizability and first hyperpolarizability of the NaH molecule obtained through the many-body perturbation-theory, coupled cluster and quadratic configuration interaction methods, including vibrational corrections. It is shown that the nuclear relaxation contribution is of fundamental importance for both polarizability and first hyperpolarizability of this system. Besides, inclusion of electron correlation effects changes appreciably the size of this contribution. In addition, our results show that the curvature contribution does not alter significantly the values obtained for the polarizability.     

Trends in the electronic and vibrational contributions to the dipole moment,polarizabilities, and first and second hyperpolarizabilities of the hydrides of Li,Na and K

The dipole moments μ, polarizabilities α, and first and second hyperpolarizabilities, β and γ of LiH, NaH and KH (MeH) have been computed using Hartree-Fock, MP2 and CCSD(T) theories. The static electronic and vibrational contributions to these properties are presented. The vibrational properties have been analysed into contributions due to zero-point vibrational averaging and pure vibrational terms. An alternative dissection of the vibrational properties into nuclear relaxation and curvature terms has also been considered. KH has been selected as a model system to study how the number of electrons, which are correlated (2, 10 and 20) affect both electronic and vibrational properties. The 10 electron approximation gives results that are practically the same as those computed by taking into account all 20 electrons of KH. The double-harmonic approximation has been shown to give satisfactory results for the pure vibrational contributions to the polarizability and the first hyperpolarizability, while this approximation is useful for demonstrating, qualitatively, the significance of the pure vibrational contributions to the second hyperpolarizability. In many cases the vibrational contributions are rather small percentages of the corresponding electronic contribution. However, several exceptions to the above observation have been noted. In all the cases considered the vibrational properties should be computed if reasonably accurate property values are sought. Electron correlation is important for both electronic and vibrational contributions to the electrical properties of the hydrides considered. The results are in satisfactory agreement with most of the best theoretical and experimental data concerning bond lengths, vibrational frequencies and electrical properties.     

Theoretical analysis on structural,spectroscopic, and electronic properties of some 2-aminobenzimidazole complexes by using PBE1PBE,B3LYP,and HF methods

The molecular geometry, vibrational frequencies, gauge including atomic orbital (GIAO) ¹H and ¹³C chemical shift values of ABZ-TNB [ABZ-TNB: 2-aminobenzimidazole-trinitrobenzene] and ABZ-PA [ABZ-PA: 2-aminobenzimidazole-picric acid] in the ground state were calculated by using density functionals (B3LYP and PBE1PBE) and Hartree-Fock (HF) methods with the 6–31 ++ G(d,p) basis set. Furthermore, the electronic spectrum of title complexes was calculated with the time dependent DFT levels (TD-PBE1PBE and TD-B3LYP) and HF (TD-HF) method starting from the ground state geometry optimized in the gas phase. A detailed assignment of vibrational spectra was made on the basis of the calculated potential energy distribution (PED). Total static dipole moment (μ), the mean polarizability (〈α〉), the anisotropy of the polarizability (Δα), the mean first-order hyperpolarizability (〈β〉), highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies, chemical hardness (η) and electronegativity (χ) of ABZ-TNB and ABZ-PA complexes were also investigated with quantum chemical calculations. Additionally, data obtained from quantum chemical calculations were compared with the experimental ones.     

The role of the electrostatic interaction in shifting the vibrational frequencies for two adsorbed molecules

We use a simple model to compute the shift of the vibrational frequencies of two adsorbed molecules as a function of inter-molecular distance, and various molecular and metal parameters. We assume that the atoms posses static and dynamic charges and the molecule has an electronic polarizability. The chemical bonds are described by Morse potentials. The electrostatic interactions are computed by a density functional method. We conclude that the use of vibrating point dipoles and of the image theorem in such calculations is an oversimplification.     

Influence of alkali metal superoxides on structure,electronic,and optical properties of Be_(12)O_(12) nanocage:Density functional theory study

The effect of alkali metal superoxides M_3O(M = Li,Na,K) on the electronic and optical properties of a Be_(12)O_(12) nanocage was studied by density functional theory(DFT) and time-dependent density functional theory(TD-DFT).The energy gaps(Eg) of all configurations were calculated.Generally,the adsorption of alkali metal superoxides on the Be_(12)O_(12) nanocage causes a decrease of Eg.Electric dipole moment μ,polarizability α,and static first hyperpolarizability β were calculated and it was shown that the adsorption of alkali metal superoxides on Be_(12)O_(12) increases its polarizability.It was found that the absorption of M_3 O on Be_(12)O_(12) nanocluster improves its nonlinear optical properties.The highest first hyperpolarizability(β≈ 214000 a.u.) is obtained in the K_3O–Be_(12)O_(12)nanocluster.The TD-DFT calculations were performed to investigate the origin of the first hyperpolarizabilities and it was shown that a higher first hyperpolarizability belongs to the structure that has a lower transition energy.     

4-N-甲基苯乙烯砒啶盐衍生物振动超极化率的理论研究

在双谐振子近似下，利用耦合微扰Hartree-Fock方法计算了4-N-甲基苯乙烯砒啶盐衍生物分子的静态振动第一超极化率和红外与拉曼光谱，给出了对静态振动第一超极化率起主导贡献的两种简正振动模式. 研究发现，标题分子的静态振动第一超极化率都比较大，且与静态电子第一超极化率呈较好的线性关系. 首次提出了利用红外与拉曼光谱特征峰标识的振动模来估算振动第一超极化率大小的少模方法. 结果表明，少模方法用于估算振动第一超极化率的大小是可行的.     

Electronic second hyperpolarizability of the carbon tetrachloride molecule

The electronic second hyperpolarizability γ of the carbon tetrachloride molecule is calculated by the ab initio molecular orbital method considering electron correlation with large basis sets. The static electronic γ value with the CCSD(T) method is 1.65 times the Hartree-Fock value, indicating a considerable electron correlation effect. Taking account of the frequency dispersion and vibrational effects, we estimate the most probable theoretical γ value at 800 nm to be around 17900au (9.0 × 10^?36 esu). On the other hand, the experimental value recently observed by optical Kerr effect method is 10.6 × 10^?36 esu at 800nm. It is concluded that the major part of the experimental χ⁽³⁾ value of carbon tetrachloride can account for the static electronic hyperpolarizability.     

Breit-Pauli and direct perturbation theory calculations of relativistic helium polarizability.

Large Gaussian-type geminal wave function expansions and direct perturbation theory (DPT) of relativistic effects have been applied to calculate the relativistic contribution to the static dipole polarizability of the helium atom. It has been demonstrated that DPT is superior for this purpose to traditional Breit-Pauli calculations. The resulting value of the molar polarizability of 4He is 0.517254(1) cm3 x mol(-1), including a literature estimate of QED effects. As a by-product, a very accurate value of the nonrelativistic helium second hyperpolarizability, gamma = 43.104227(1) atomic units (without the mass-polarization correction), has been obtained.     

Application of the polarizable-ion model on crystals with the corundum structure

This paper reports the results of charge, polarizability and force constant calculations at k? = 0 on crystals with the corundum structure. Published vibrational frequencies are used in the normal coordinate treatment. The calculated electronic parameters are discussed.     

轮烯衍生物电子结构及三阶非线性光学性质的理论研究

苯轮烯衍生物具有良好的非线性光学性质. 运用密度泛函理论在不同理论水平和不同基组下计算了轮烯衍生物的静态极化率α和静态第二超极化率γ. 采用含时密度泛函TD-B3LYP方法计算了轮烯分子的紫外吸收光谱. 结果发现: 弥散函数对静态线性极化率α和第二超极化率γ 的计算结果都有显著的影响; 共轭体系的大小和引入的推拉电子基团可以调节轮烯衍生物的第二超极化率. 添加推拉电子基团后不仅能得到更高的非线性光学系数, 也能保证有较好的透光性能, 表明轮稀分子兼具有较高的三阶非线性光学响应和在可见光波段具有良好的透光性的特性. 此外, 采用CAM-B3LYP方法计算了分子1-1和分子2-2的动态(超)极化率. 计算结果表明: 在近红外区, 随着入射光频率的增大, α (ω; ω), γ (-ω; ω, 0, 0) 和γ (-2ω; ω, ω, 0) 都随之增大, 出现近共振增强效应; 在远离共振条件下, α (ω; ω), γ (-ω; ω, 0, 0) 和γ (-2ω; ω, ω, 0) 变化平缓.     

Calculation of the dipole hyperpolarizability of atoms with closed and open shells by the Hartree-Fock-Roothaan method

The Hartree-Fock-Roothaan method is extended to the calculation of the hyperpolarizability of atoms. The static polarizability and hyperpolarizability of some atoms with closed and open shells are calculated using an optimized basis set of Slater-type atomic orbitals. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 1, pp. 5–12, January–February, 2008.     

Dispersion of the third-order susceptibility of a cyanine dye measured by coherent anti-Stokes Raman scattering

The dispersion of the third-order susceptibility of the cyanine dye bis-(dimethylamino)-heptamethinium chloride was measured by Coherent Anti-Stokes Raman Scattering (CARS) over a wide wavelength range from 530 to 830 nm. Large negative values of the real part of the second-order hyperpolarizability are observed. The data are analyzed with the help of theoretical calculations based on a perturbative approach for the nonlinearities. The dispersion behavior of the third-order susceptibility is governed by the resonant enhancement due to vibrational transitions of the first excited electronic state and, to lesser extent, by an electronic two-photon resonance around 600 nm.     

Effect of separation on second-order hyperpolarizability of two silver nanoclusters

We present a study on dielectric response of Ag₁₄ nanocluster dimer using first principles methods. The interaction energy, (hyper)polarizability of dimer are predicted under various separations of the two identical Ag₁₄ nanoclusters. The appropriate separation makes the second-order hyperpolarizability of Ag₁₄ dimer is about 70 times larger than the Ag₁₄ monomer. The increase of polarizability and hyperpolarizability is ascribed to reconfiguration of molecular electronic state from Ag cluster monomer to dimer. Nonlinear response is more susceptible to the steady intermediate state compared to linear response. The crucial transitions contributed to hyperpolarizability are assigned to be from highest occupied molecular orbitals to the lowest unoccupied molecular orbital (HOMOs-LUMO) of nanocluster dimer. Binding character of LUMO plays an important role in determining nonlinear optical properties.     

An ab initio study of vibrational corrections to the electrical properties of ethylene

Accurate SCF and MP2 quartic property hypersurfaces have been computed for the energy, quadrupole moment and polarizability tensor of ethylene to obtain zero-point vibrational corrections to the properties. Coupled with accurate electrical properties computed at a high level correlated r _e geometry, using a range of correlated methods, especially BD and BD(T), along with a number of purpose-built polarized basis sets, definitive estimates have been made of these properties that incorporate the effects of vibrational averaging. The effect of deuterium substitution on the properties was investigated, and the frequency dependence of the polarizability tensor was studied also. Careful attention has been paid to a critical comparison between these theoretical estimates and experimental measurements, and agreement between the two is shown to be exceptionally good. In particular, it is possible to resolve the disagreement between recent theoretical calculations and experimental measurements of the Cotton–Mouton constant. The results focus attention on both the general utility of the present method, and the necessity to allow for the effects of zero-point vibrational averaging when comparing theory with experiment, or even when comparing different theoretical results with one another using experiment as a benchmark.     

Finite-field calculations of molecular polarizabilities using field-induced polarization functions: second- and third-order perturbation correlation corrections to the coupled Hartree-Fock polarizability of H2O

Ordinary Rayleigh-Schrödinger perturbation theory with Møller-Plesset (RSMP) partitioning is used to calculate second- and third-order correlation corrections to the CHF polarizability and dipole moment of the water molecule by a finite-field procedure. [2/1] Padé approximants are found to be useful in accelerating the convergence of the property perturbation expansions. Field-induced polarization functions suitable for polarizability calculations are determined. The average polarizability calculated, neglecting vibrational averaging, with Dunning's (9s5p/4s-4s2p/2s) contracted GTO basis set augmented by field-induced 1s1p2d/1p polarization functions is within 3 per cent of the experimental result. Correlation corrections to the dipole moment and polarizability of the water molecule calculated by the finite-field RSMP and single + double excitation CI(SDCI) methods for the same basis set are found to be in close agreement. The RSMP approach has the advantages of being size-consistent and of being capable of greater efficiency than the SCDI method. Comparative calculations carried out using Epstein-Nesbet partitioning show that through third order RSEN correlation perturbation expansions for the dipole moment and polarizability are less rapidly convergent than RSMP expansions. However, reasonable accord with RSMP results can be achieved by using [2/1] Padé approximants to accelerate the convergence of RSEN energy perturbation expansions. The convergence of RSMP property correlation expansions based on the zeroth-order uncoupled-Hartree-Fock (UCHF) and coupled-Hartree-Fock (CHF) approximations are compared through third order. Whereas the CHF + RSMP expansions are for practical purposes fully converged, the UCHF + RSMP expansions are not adequately converged.     

Alkali-induced enhancement of surface electronic polarizibility

From results of ab initio electronic structure calculations based on density functional theory for a set of prototype systems, we find alkali adsorbates to cause a dramatic enhancement of the electronic polarizability of the metal surface extending it several angstroms into the vacuum. This phenomenon is traceable to an unusual feature induced in the surface potential on alkali adsorption. The effect appears to be general, as we find it to be present on metals as varied as Pd and Cu, and helps explain the observed substantial decrease in the vibrational frequency of molecules when coadsorbed with alkalis on metal surfaces. Specifically, for two dissimilar molecules CO and O(2), we trace the softening of the frequencies of their stretching mode when coadsorbed with K on Pd(111) to the enhanced electronic polarizability.     

Convergence of experiment and theory on the pure vibrational spectrum of HeH(+)

Very accurate quantum mechanical calculations of the pure vibrational spectrum of the molecular ion are reported and compared with newly obtained pure vibrational transitions extracted from the available experimental data. The calculations are performed without assuming the Born-Oppenheimer approximation regarding separability of the nuclear and electronic motions and include the first order relativistic mass-velocity and Darwin corrections. For the two lowest transitions, whose experimental energies are established with the highest precision, the calculated and the experimental results show very good agreement.     

Evaluation of the second order strain derivatives of the electronic dielectric constant of alkali halides

We have evaluated the second order strain derivatives of the electronic dielectric constant of alkali halides employing two different theories viz. the Clausius—Mossotti theory of polarizability and the Penn model of energy gap. The results obtained from the two theories are in fair agreement with each other. It has been emphasised that the present calculations can be used to separate the electronic and ionic contributions to the second order strain derivative of the static dielectric constant.