Effects of different basis sets and donor‐acceptor groups on linear and second‐order nonlinear optical properties and molecular frontier orbital energies

The calculation of molecular hyperpolarizability, molecular frontier orbital energies of some donor‐acceptor oxadiazoles ( 5a – f , 8a – f , and 9a – f ) have been investigated using ab initio methods and different basis sets. Ab initio optimizations were performed at the Hartree–Fock (HF) and density functional (Beckee‐3–Lee–Yang–Parr; B3LYP) levels of theory with 6‐31G basis set. The polarizability (<α>), anisotropy of polarizability (Δα), and ground‐state dipole moment (μ), first hyperpolarizability (β), and molecular frontier orbital (HOMO, highest occupied molecular orbital and LUMO, lowest unoccupied molecular orbital) energies of 5a – f , 8a – f , and 9a – f have been calculated at the HF and B3LYP methods with 6‐31G, 6‐31G(d), 6‐31+G(d), 6‐31++G(d,p), 6‐311G, 6‐311G(d), 6‐311+G(d), and 6‐311++G(d,p) basis sets. Also, the molecular hardness (η) and electronegativity (χ) parameters have been obtained using molecular frontier orbital energies. The <α>, Δα, μ, β, HOMO, LUMO energies, η and χ parameters have been investigated as dependence on the choice of method and basis set. The variation graphics of <α>, Δα, μ, β, η, and χ parameters using HF and B3LYP methods with different basis sets are presented. We have examined the frontier molecular orbital pictures of 5a – f , 8a – f , and 9a – f using B3LYP/6‐31++G(d,p) level. The 5a – f , 8a – f , and 9a – f display significant linear, second‐order molecular nonlinearity, and molecular parameters and provide the basis for future design of efficient nonlinear optical materials having the 1,3,4‐oxadiazole core. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Bonding and (hyper)polarizability in the sodium dimer

We report a conventional ab initio and density functional theory study of the polarizability (alpha(alphabeta)/e(2)a(0) (2)E(h) (-1)) and hyperpolarizability (gamma(alphabetagammadelta)/e(4)a(0) (4)E(h) (-3)) of the sodium dimer. A large [18s14p9d2f1g] basis set is thought to yield near-Hartree-Fock values for both properties: alpha=272.28, Deltaalpha=127.22 and gamma=2157.6 x 10(3) at R(e)=3.078 87 A. Electron correlation has a remarkable effect on the Cartesian components of gamma(alphabetagammadelta). Our best value for the mean is gamma=1460.1 x 10(3). The (hyper)polarizability shows very strong bond-length dependence. The effect is drastically different for the longitudinal and transverse components of the hyperpolarizability. The following first derivatives were extracted from high-level coupled cluster calculations: (dalpha/dR)(e)=54.1, (dDeltaalpha/dR)(e)=88.1e(2)a(0)E(h) (-1), and (dgamma/dR)(e)=210 x 10(3)e(4)a(0) (3)E(h) (-3). We associate the (hyper)polarizability to bonding effects between the two sodium atoms by introducing the differential property per atom Q(diff)/2 identical with (Q[Na(2)(X (1)Sigma(g) (+))]/2-Q[Na((2)S)]). The differential (hyper)polarizability per atom is predicted to be strongly negative for the dimer at R(e), as [alpha(Na(2))/2-alpha(Na)]=-33.8 and [gamma(Na(2))/2-gamma(Na)]=-226.3 x 10(3). The properties calculated with the widely used B3LYP and B3PW91 density functional methods differ significantly. The B3PW91 results are in reasonable agreement with the conventional ab initio values. Last, we observe that low-level ab initio and density functional theory methods underestimate the dipole polarizability anisotropy. Experimental data on this important property are highly desirable.     

Efficient polarized basis sets for evaluation of static and dynamic molecular electric properties

New medium size Gaussian‐type basis set R‐ORP for evaluation of static and dynamic electric properties in molecular systems is presented. It is obtained in a close resemblance to the original ORP basis set, from the source basis set through addition of two first‐order polarization functions whose exponent values are optimized with respect to the finite field restricted open‐shell Hartree–Fock (ROHF) atomic polarizabilities. As the source set the VTZ basis set of Ahlrichs and coworkers, augmented with additional diffuse functions and contracted to the form [6s/3s] for hydrogen and [11s7p/4s3p] for carbon through fluorine, is chosen. The resulting basis set is of the form [6s2p/3s2p] for hydrogen and [11s7p2d/4s3p2d] for other atoms. Presented basis set is next tested in the CCSD static and dynamic molecular polarizability and hyperpolarizability calculations for a set of ten and four test molecules, respectively, for which very accurate reference data exist. Additionally, the recently developed ORP basis set is employed in the calculations to examine the limits of its applicability. Results are compared to the literature data obtained in both, large and diffuse, as well as reduced‐size basis sets. In the case of polarizability calculations, the aug‐pc‐1 and R‐ORP are the optimal choices among the investigated smaller basis sets, with the overall performance of the aug‐pc‐1 set being better. Among the larger sets, the ORP performs better in the case of average polarizability, while the RMSE values for polarizability anisotropy are practically identical for d‐aug‐cc‐pVDZ and ORP sets. Finally, the R‐ORP and ORP basis sets compete other small bases in the evaluation of the first hyperpolarizability in investigated systems. © 2016 Wiley Periodicals, Inc.     

Model systems for probing metal cation hydration: the V+(H2O) and ArV+(H2O) complexes

In support of mass-selected infrared photodissociation (IRPD) spectroscopy experiments, coupled-cluster methods including all single and double excitations (CCSD) and a perturbative contribution from connected triple excitations [CCSD(T)] have been used to study the V+(H2O) and ArV+(H2O) complexes. Equilibrium geometries, harmonic vibrational frequencies, and dissociation energies were computed for the four lowest-lying quintet states (5A1, 5A2, 5B1, and 5B2), all of which appear within a 6 kcal mol(-1) energy range. Moreover, anharmonic vibrational analyses with complete quartic force fields were executed for the 5A1 states of V+(H2O) and ArV+(H2O). Two different basis sets were used: a Wachters+f V[8s6p4d1f] basis with triple-zeta plus polarization (TZP) for O, H, and Ar; and an Ahlrichs QZVPP V[11s6p5d3f2g] and Ar[9s6p4d2f1g] basis with aug-cc-pVQZ for O and H. The ground state is predicted to be 5A1 for V+(H2O), but argon tagging changes the lowest-lying state to 5B1 for ArV+(H2O). Our computations show an opening of 2 degrees -3 degrees in the equilibrium bond angle of H2O due to its interaction with the metal ion. Zero-point vibrational averaging increases the effective bond angle further by 2.0 degrees -2.5 degrees, mostly because of off-axis motion of the heavy vanadium atom rather than changes in the water bending potential. The total theoretical shift in the bond angle of about +4 degrees is significantly less than the widening near 9 degrees deduced from IRPD experiments. The binding energies (D0) for the successive addition of H2O and Ar to the vanadium cation are 36.2 and 9.4 kcal mol(-1), respectively.     

PH~3...H~2O体系分子间相互作用的从头计算MO研究

在MP2/6-311++G(3d,3p)水平,对PH~3...H~2O体系可能存在的氢键复合物进行了全自由度能量梯度优化,发现PH~3...H~2O体系存在三个能量极小结构A,B和C。其中结构A和B以H~2O作为质子授体,结构C以PH~3作为质子授体,结构A较结构B和C分别稳定6.52kJ/mol和8.18kJ/mol。结构A具有C~s对称性,其结构中P原子和O原子间距离为354.78nm,键角OHP为171.35ⅲ,属于接近于直线的传统型氢键结构。进一步在高级电子相关校正的MP4SDTQ下,用6-311++G(3df,3pd)基加上键函数{3s3p2d1f},通过BSSE校正,精确计算了结构A的结合能为-10.84kJ/mol。     

高级量子化学从头计算法研究N2和H2O分子间相互作用

在MP2/6-311++G(3d,3p)电子相关校正水平上,对N₂和H₂O分子间可能存在的氢键复合物进行全自由度能量梯度优化,发现了一个接近于直线的弱氢键总能量极小结构(1),进一步在高级电子相关校正的MP4SDTQ和CCSD(T)水平,用6-311++G(3d,3p)基组加上(3s3p2d1f)键函数,用MP4和CCSD(T)计算的结构1的结合能分别为-5.061kJ/mol和-4.715kJ/mol.     

Reduced-size polarized basis sets for calculations of molecular electric properties. IV. First-row transition metals

Recent studies of the perturbation-dependent basis sets have indicated the possibility of a significant reduction of the size of the usual CGTO sets without considerable loss of accuracy in calculations of molecular electric properties. The resulting (ZPolX) basis sets have been developed for several atoms of the first and second row of the Periodic Table. The same method of the ZPolX basis set generation is extended for the first-row transition metals and the corresponding contracted ZPolX basis sets of the size [6s5p3d1f] are determined for both nonrelativistic and scalar relativistic calculations. The performance of the ZPolX basis sets is verified in calculations on the first-row transition metal oxides at the level of the ROHF, ROHF/CASPT2, and ROHF/CCSD(T) approximations. Also the study of the dipole polarizability of TiCl₄ confirms the excellent features of these very compact basis sets. The ZPolX basis sets for nonrelativistic and relativistic calculations of molecular electric properties are available on the web page http://www.chem.uni.torun.pl/zchk/basis-sets.html.     

Dielectric Relaxation Around a Charged Colloidal Cylinder in an Electrolyte

The polarizability and corresponding dielectric relaxation of the Debye-Hückel (DH) atmosphere surrounding a charged rod-like polyelectrolyte immersed in an ionic solution of a symmetrical electrolyte is determined following the method developed by J. A. Fornés [Phys. Rev. E 57, 2110 (1998)]. Several formulas are given to estimate the DH atmosphere parameters, namely, the polarizability at zero frequency, alpha(0), the relaxation time, tau, the cloud capacitance, C, the average displacement of the ionic cloud, delta, the square root dipole moment quadratic fluctuation, (1/2), and the thermal fluctuating field, (1/2). The Poisson-Boltzmann equation is solved numerically to apply the theory to a highly charged polyelectrolyte such as DNA in solution, although formulas valid for the DH approximation are also given. A dispersion in the polarizability and correspondingly in the dielectric constant of these solutions in the microwave region is predicted. For instance, considering a DNA length of 1000 ?, with its reduced linear charge density xi(0)=4.25 and ionization factor gamma=0.5, immersed in a NaCl solution (40 mM), we predict a polarizability of the DH atmosphere at zero frequency alpha(0) of 1x10(-33) Fm(2) ( approximately 6.1x10(6)) times greater than the mean value of the polarizability of water) and the corresponding fluctuating dipole moment p of 2.1x10(-27) Cm ( approximately 600 times greater than the permanent dipole moment of water molecule). The relaxation time and the average displacement of the ionic cloud are tau=1.6 ns and delta=14. ?, respectively. This displacement is produced by the thermal fluctuating field, which, in this case, at room temperature is (1/2)=2 x10(6) V/m. Copyright 2000 Academic Press.     

Global potential energy surfaces for O((3)P) + H2O((1)A1) collisions

Global analytic potential energy surfaces for O((3)P) + H(2)O((1)A(1)) collisions, including the OH + OH hydrogen abstraction and H + OOH hydrogen elimination channels, are presented. Ab initio electronic structure calculations were performed at the CASSCF + MP2 level with an O(4s3p2d1f)/H(3s2p) one electron basis set. Approximately 10(5) geometries were used to fit the three lowest triplet adiabatic states corresponding to the triply degenerate O((3)P) + H(2)O((1)A(1)) reactants. Transition state theory rate constant and total cross section calculations using classical trajectories to collision energies up to 120?kcal mol(-1) (～11?km s(-1) collision velocity) were performed and show good agreement with experimental data. Flux-velocity contour maps are presented at selected energies for H(2)O collisional excitation, OH + OH, and H + OOH channels to further investigate the dynamics, especially the competition and distinct dynamics of the two reactive channels. There are large differences in the contributions of each of the triplet surfaces to the reactive channels, especially at higher energies. The present surfaces should support quantitative modeling of O((3)P) + H(2)O((1)A(1)) collision processes up to ～150?kcal mol(-1).     

Au+(1S, 3D)与N2O(1Σ+)反应机理的理论研究

采用密度泛函B3LYP方法, O和N用6-311+G*基组, Au+用赝势基组(8s7p6d)/[6s5p3d], 研究了Au+(1S, 3D)离子和N2O(1Σ+)分子的反应机理. 报道了在基态单重态和激发三重态势能面上各反应物、中间体和过渡态的构型特征及能量. 结果表明, 两个主反应通道Au+(1S)+ N2O(1Σ+)→1NA-Complex-1→1NA-TS1→1NA-Complex-2→1NA-Crossing→[3OAuNN]+和Au+(1S)+ N2O(1Σ+)→1NB-Complex→1NB-Crossing→[AuNN(1Σ+)]++O(3P)都需经过反应交叉势能面, 出现“系间窜越”. 用内禀坐标单点计算垂直激发态的方法确定了势能面交叉点, 并用含时密度泛函TD-B3LYP方法进一步探讨了自旋翻转机理.     

Full configuration interaction calculation of BeH adiabatic states

An all-electron full configuration interaction (FCI) calculation of the adiabatic potential energy curves of some of the lower states of BeH molecule is presented. A moderately large ANO basis set of atomic natural orbitals (ANO) augmented with Rydberg functions has been used in order to describe the valence and Rydberg states and their interactions. The Rydberg set of ANOs has been placed on the Be at all bond distances. So, the basis set can be described as 4s3p2d1f3s2p1d(BeH)+4s4p2d(Be). The dipole moments of several states and transition dipole strengths from the ground state are also reported as a function of the R(Be-H) distance. The position and the number of states involved in several avoided crossings present in this system have been discussed. Spectroscopic parameters have been calculated from a number of the vibrational states that result from the adiabatic curves except for some states in which this would be completely nonsense, as it is the case for the very distorted curves of the 3s and 3p (2)Sigma(+) states or the double-well potential of the 4p (2)Pi state. The so-called "D complex" at 54 050 cm(-1) (185.0 nm) is resolved into the three 3d substates ((2)Sigma(+),(2)Pi,(2)Delta). A diexcited valence state is calculated as the lowest state of (2)Sigma(-) symmetry and its spectroscopic parameters are reported, as well as those of the 2 (2)Delta (4d) state The adiabatic curve of the 4 (2)Sigma(+) state shows a swallow well at large distances (around 4.1 A) as a result of an avoided crossing with the 3 (2)Sigma(+) state. The probability that some vibrational levels of this well could be populated is discussed within an approached Landau-Zerner model and is found to be high. No evidence is found of the E(4ssigma) (2)Sigma(+) state in the region of the "D complex". Instead, the spectroscopic properties obtained from the (4ssigma) 6 (2)Sigma(+) adiabatic curve of the present work seem to agree with those of the experimental F(4psigma) (2)Sigma(+) state. The FCI calculations provide benchmark results for other correlation models for the open-shell BeH system and evidence both the limitations and capabilities of the basis set.     

Frequency-dependence of the polarizability anisotropy of CO2 revisited

We present extended determinations of the polarizability anisotropy κ(ω) of CO₂ at 514.5 and 488.0 nm by means of measuring the depolarization ratio ρ(ω) of linearly polarized laser light. Taking into account the hitherto reported data on ρ(ω) as well as experimental data on the mean polarizability (ω) and additional information derived from Kerr-effect measurements, we obtain a value of the static polarizability anisotropy of CO₂ of κ(0)=15.2(1.6) au. The large uncertainty of ≈10% results from the fact that all available experimental information is used to obtain an estimate of the static polarizability ansiotropy of CO₂. This zero-frequency value, which includes the vibrational part of the static anisotropy, is in reasonable agreement with hitherto reported experimental data and in good accordance with new ab initio calculations.     

Approaching actinide(+III) hydration from first principles

A systematic computational approach to An(III) hydration on a density-functional level of theory, using quasi-relativistic 5f-in-core pseudopotentials and valence-only basis sets for the An(III) subsystems, is presented. Molecular structures, binding energies, hydration energies, and Gibbs free energies of hydration have been calculated for [An(III)(OH(2))(h)](3+) (h = 7, 8, 9) and [An(III)(OH(2))(h-1) * OH(2)](3+) (h = 8, 9), using large (7s6p5d2f1g)/[6s5p4d2f1g] An(III) and cc-pVQZ O and H basis sets within the COSMO implicit solvation model. An(III) preferred primary hydration numbers are found to be 8 for all An(III) at the gradient-corrected density-functional level of theory. Second-order M?ller-Plesset perturbation theory predicts preferred primary hydration numbers of 9 and 8 for Ac(III)-Md(III) and No(III)-Lr(III), respectively.     

Quasirelativistic energy-consistent 4f-in-core pseudopotentials for tetravalent lanthanide elements

Quasirelativistic energy-consistent 4f-in-core pseudopotentials modeling tetravalent lanthanides (4f ^n?1 occupation with n = 1, 2, 3, 8, 9 for Ce, Pr, Nd, Tb, Dy) have been adjusted. Energy-optimized (6s5p4d) and (7s6p5d) valence basis sets contracted to polarized double- to quadruple-zeta quality as well as 2f1g correlation functions have been derived. Corresponding smaller (4s4p3d) and (5s5p4d) basis sets suitable for calculations on lanthanide(IV) ions in crystalline solids form subsets of these basis sets designed for calculations on neutral molecules. Calculations for lanthanide tetrafluorides using the 4f-in-core pseudopotentials at the Hartree–Fock level show satisfactory agreement with calculations using 4f-in-valence pseudopotentials. For cerium tetrafluoride the experimental bond length is well reproduced using the 4f-in-core pseudopotential at the coupled-cluster level with single and double excitation operators and a perturbative estimate of triple excitations. For cerium dioxide 4f-in-core and 4f-in-valence pseudopotential calculations agree quite well, if a proper f basis set instead of f polarization functions is applied.     

Structure and stability of salicylic acid-water complexes and the effect of molecular hydration on the spectral properties of salicylic acid

Density functional theory with B3LYP parametrization and 6-311++G(d,p) basis set has been used to investigate the structure and stability of salicylic acid-water complexes. The vertical excitation energies for these complexes have been computed using time-dependent density functional theory (with B3LYP parametrization and a 6-311++G(d,p) basis set). It is shown that the hydrogen bond between the carboxylic hydrogen and the oxygen of water is the strongest among all possible hydrogen bonds in the system. The hydrogen bond strength in salicylic acid-water complexes seems to be nearly additive. The change in absorption maximum (lambda(max)) corresponding to the vertical excitation energy for the first three excited singlet and triplet states of the complex with 1-3 water molecules is nominal (approximately 1-3 nm). But with the addition of the fourth water molecule, the lambda(max) for S(1) and T(1) decreases by approximately 17 nm and it increases for S(2) and S(3) by about the same amount. The decrease in lambda(max) for transition to the T(2) state on the addition of the fourth water molecule is only approximately 9 nm. There seems to be an intersystem crossing between the S(1) and T(3) states that could account for the observed fluorescence quenching of salicylic acid in water.     

Complete basis set extrapolated potential energy, dipole, and polarizability surfaces of alkali halide ion-neutral weakly avoided crossings with and without applied electric fields

Complete basis set extrapolations of alkali halide (LiF, LiCl, NaF, NaCl) energy, dipole, and polarizability surfaces are performed with and without applied fields along the internuclear axis using state-averaged multireference configuration interaction. Comparison between properties (equilibrium separation, dissociation energy, crossing distance, diabatic coupling constant, dipole, and polarizability) derived from the extrapolated potential energy (or dipole) surfaces are made with those obtained from direct extrapolation from the basis set trends. The two extrapolation procedures are generally found to agree well for these systems. Crossing distances from this work are compared to those of previous work and values obtained from the Rittner potential. Complete basis set extrapolated crossing distances agree well with those derived from the Rittner potential for LiF, but were significantly larger for LiCl, NaF, and NaCl. The results presented here serve as an important set of benchmark data for the development of new-generation many-body force fields that are able to model charge transfer.