Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell pi-conjugated systems

The basis set and electron correlation effects on the static polarizability (alpha) and second hyperpolarizability (gamma) are investigated ab initio for two model open-shell pi-conjugated systems, the C(5)H(7) radical and the C(6)H(8) radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C(6)H(8) whereas diffuse functions are compulsory for C(5)H(7), in particular, p diffuse functions. In addition to the 6-31G(*)+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for alpha and gamma of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order M?ller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order M?ller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order M?ller-Plesset method, provide for both compounds gamma values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged alpha and gamma values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of alpha and gamma have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.     

Linear and non-linear optical properties of some donor–acceptor oxadiazoles by ab initio Hartree-Fock calculations

The molecular hyperpolarizability of some donor–acceptor oxadiazoles was investigated using ab initio methods. Ab initio optimizations were performed at the Hartree-Fock level using different basis sets, starting with the minimal basis set, and then split valence sets. The first hyperpolarizabilities were calculated at the Hartree-Fock level employing the corresponding basis sets using Gaussian 98W. In general, the first hyperpolarizability is dependent on the choice of method and basis set. In order to understand this phenomenon in the context of molecular orbital picture, we examined the molecular HOMOs and molecular LUMOs generated via HF/6-31G level. It has also been calculated the polarizability, anisotropy of polarizability and ground state dipole moment of all the molecules. Several of these oxadiazoles display significant second-order molecular nonlinearity, β(8.57–195.05 × 10⁻³⁰ esu) and provide the basis for future design of efficient nonlinear optical materials having the oxadiazole core.     

Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: where it is shown how finite oligomer chains tend to the infinite periodic polymer

The longitudinal polarizability, α(xx), and second hyperpolarizability, γ(xxxx), of polyacetylene are evaluated by using the coupled perturbed Hartree-Fock/Kohn-Sham (HF/KS) scheme as implemented in the periodic CRYSTAL code and a split valence type basis set. Four different density functionals, namely local density approximation (LDA) (pure local), Perdew-Becke-Ernzerhof (PBE) (gradient corrected), PBE0, and B3LYP (hybrid), and the Hartree-Fock Hamiltonian are compared. It is shown that very tight computational conditions must be used to obtain well converged results, especially for γ(xxxx), that is, very sensitive to the number of k(->) points in reciprocal space when the band gap is small (as for LDA and PBE), and to the extension of summations of the exact exchange series (HF and hybrids). The band gap in LDA is only 0.01 eV: at least 300 k(->) points are required to obtain well converged total energy and equilibrium geometry, and 1200 for well converged optical properties. Also, the exchange series convergence is related to the band gap. The PBE0 band gap is as small as 1.4 eV and the exchange summation must extend to about 130 A? from the origin cell. Total energy, band gap, equilibrium geometry, polarizability, and second hyperpolarizability of oligomers -(C(2)H(2))(m)-, with m up to 50 (202 atoms), and of the polymer have been compared. It turns out that oligomers of that length provide an extremely poor representation of the infinite chain polarizability and hyperpolarizability when the gap is smaller than 0.2 eV (that is, for LDA and PBE). Huge differences are observed on α(xx) and γ(xxxx) of the polymer when different functionals are used, that is in connection to the well-known density functional theory (DFT) overshoot, reported in the literature about short oligomers: for the infinite model the ratio between LDA (or PBE) and HF becomes even more dramatic (about 500 for α(xx) and 10(10) for γ(xxxx)). On the basis of previous systematic comparisons of results obtained with various approaches including DFT, HF, Moller-Plesset (MP2) and coupled cluster for finite chains, we can argue that, for the infinite chain, the present HF results are the most reliable.     

Theoretical investigation of the (hyper)polarizabilities of pyrrole homologues C4H4XH (X = N, P, As, Sb, Bi). A coupled-cluster and density functional theory study

Geometries, inversion barriers, static and dynamic electronic and vibrational dipole polarizability (alpha), and first (beta) and second (gamma) hyperpolarizability of the pyrrole homologues C(4)H(4)XH (X = N, P, As, Sb, Bi) have been calculated by Hartree-Fock, M?ller-Plesset second-order perturbation theory, coupled-cluster theory accounting for singles, doubles, and noniterative triple excitations methods, as well as density functional theory using B3LYP and PBE1PBE functionals and Sadlej's Pol and 6-311G basis sets. Relativistic effects on the heavier homologues stibole and bismole have been taken into account within effective core potential approximation. The results show that the electronic (hyper)polarizabilities monotonically increase with the atomic number of the heteroatom, consistent with the decrease in the molecular hardness. Ring planarization reduces the carbon-carbon bond length alternation of the cis-butadienic unit, enhancing the electronic polarizability values (alpha(e)) by 4-12% and the (hyper)polarizability values (and gamma(e)) by 30-90%. Pure vibrational and zero-point vibrational average contributions to the (hyper)polarizabilities have been determined within the clamped nucleus approach. In the static limit, the pure vibrational hyperpolarizabilities have a major contribution. Anharmonic corrections dominate the pure vibrational hyperpolarizabilities of pyrrole, while they are less important for the heavier homologues. Static and dynamic electronic response properties of the pyrrole homologues are comparable to or larger than the corresponding properties of the furan and cyclopentadiene homologue series.     

Ab initio finite field (hyper)polarizability computations on stoichiometric gallium arsenide clusters GanAsn (n=2-9)

We report reliable ab initio finite field (hyper)polarizability values at Hartree-Fock and second order Moller-Plesset perturbation theory (MP2) levels of theory for different geometrical configurations of small gallium arsenide clusters Ga(n)As(n) with n=2-5. We relied on all-electron basis sets and pseudopotentials suitable for (hyper)polarizability calculations. In each case, we used structures that have been established in the literature after we optimized their geometries at B3LYP/cc-pVTZ-PP level of theory. Our results suggest that the first order hyperpolarizability (beta) is much more sensitive to the special geometric features than the second order hyperpolarizability (gamma). For the most stable configurations up to ten atoms the second order hyperpolarizability at MP2 level of theory varies between 15 x 10(4) and 32 x 10(4) e(4)a0 (4)Eh(-3). In addition, we examined the polarizability per atom evolution versus the cluster size for Ga(n)As(n) with n=2-9. Our work extends earlier theoretical studies which were limited to eight atoms and exposes that the polarizability/atom of the most stable stoichiometric configurations up to Ga(9)As(9) continues the monotonic downward trend with increasing size. Lastly, from the methodological point of view, our analysis shows that apart from polarizabilities, augmented pseudopotentials yield reliable first and second hyperpolarizability values as well.     

The calculation of static polarizabilities of 1-3D periodic compounds. the implementation in the crystal code

The Coupled Perturbed Hartree-Fock (CPHF) scheme has been implemented in the CRYSTAL06 program, that uses a gaussian type basis set, for systems periodic in 1D (polymers), 2D (slabs), 3D (crystals) and, as a limiting case, 0D (molecules), which enables comparison with molecular codes. CPHF is applied to the calculation of the polarizability alpha of LiF in different aggregation states: finite and infinite chains, slabs, and cubic crystal. Correctness of the computational scheme for the various dimensionalities and its numerical efficiency are confirmed by the correct trend of alpha: alpha for a finite linear chain containing N LiF units with large N tends to the value for the infinite chain, N parallel chains give the slab value when N is sufficiently large, and N superimposed slabs tend to the bulk value. CPHF results compare well with those obtained with a saw-tooth potential approach, previously implemented in CRYSTAL. High numerical accuracy can easily be achieved at relatively low cost, with the same kind of dependence on the computational parameters as for the SCF cycle. Overall, the cost of one component of the dielectric tensor is roughly the same as for the SCF cycle, and it is dominated by the calculation of two-electron four-center integrals.     

A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error

We evaluate the performance of ten functionals (B3LYP, M05, M05-2X, M06, M06-2X, B2PLYP, B2PLYPD, X3LYP, B97D, and MPWB1K) in combination with 16 basis sets ranging in complexity from 6-31G(d) to aug-cc-pV5Z for the calculation of the H-bonded water dimer with the goal of defining which combinations of functionals and basis sets provide a combination of economy and accuracy for H-bonded systems. We have compared the results to the best non-density functional theory (non-DFT) molecular orbital (MO) calculations and to experimental results. Several of the smaller basis sets lead to qualitatively incorrect geometries when optimized on a normal potential energy surface (PES). This problem disappears when the optimization is performed on a counterpoise (CP) corrected PES. The calculated interaction energies (ΔEs) with the largest basis sets vary from -4.42 (B97D) to -5.19 (B2PLYPD) kcal/mol for the different functionals. Small basis sets generally predict stronger interactions than the large ones. We found that, because of error compensation, the smaller basis sets gave the best results (in comparison to experimental and high-level non-DFT MO calculations) when combined with a functional that predicts a weak interaction with the largest basis set. As many applications are complex systems and require economical calculations, we suggest the following functional/basis set combinations in order of increasing complexity and cost: (1) D95(d,p) with B3LYP, B97D, M06, or MPWB1k; (2) 6-311G(d,p) with B3LYP; (3) D95++(d,p) with B3LYP, B97D, or MPWB1K; (4) 6-311++G(d,p) with B3LYP or B97D; and (5) aug-cc-pVDZ with M05-2X, M06-2X, or X3LYP.     

Ab initio CPHF calculations of the static polarizability and second hyperpolarizability of small molecules: Comparisons between standard and moderately large basis sets augmented with diffuse functions

Static polarizability and second hyperpolarizability have been calculated for a number of small molecules? CO₂, OCS, CS₂, C₂H₂, C₂H₆, C₃H₈, cyclo-C₃H₆, C₃H₄, C₃H₆, SiH₄, Si₂H₆? in the framework of the coupled-perturbed Hartree-Fock (CPHF ) theory. The linear and nonlinear coefficients have been calculated with standard Gaussian basis sets and 3-21G bases moderately enlarged with diffuse functions. It is shown that the parallel component of the polarizability saturates rapidly, which suggests that a 3-21G basis containing s and p diffuse functions is sufficient to reproduce α_zz. For the α_xx and α_yy components, a 3-21G basis with s, p, and d diffuse functions is required. In general, the concordance between α computed with this basis set and the experimental static polarizability is at least of the order of 80%. On the contrary, the computation of the second hyperpolarizability with the same basis set for CO₂, CS₂, and C₂H₂ gives values that are 30% too low, compared to the experimental value. Better results are observed for ethane, propane, and cyclopropane for which the error is lower than 50%. The better agreement observed for the saturated compounds can probably be explained by their saturated character.     

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     

Radial dependence of exterior electron distributions of molecular orbitals

A molecular surface is introduced to divide interior electron densities from exterior electron densities (EED). The radial distribution of EED (RADEED) is defined for each molecular orbital as a function of the distance from the molecular surface. Logarithmic plots of RADEED for NH₃ using various basis sets in ab initio MO calculations revealed some important features: (i) the Hartree-Fock limit for the orbital function tail may be suggested and thus qualities of basis sets can be discussed, and (ii) the slope of the curve shows the decay rate of the orbital which can be compared with the curve derived from the theoretical behavior of the long-range asymptotic form involving either the lowest ionization potential or the orbital energy of the highest occupied orbital.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Theoretical investigation of the linear and second-order nonlinear susceptibilities of the 3-methyl-4-nitropyridine-1-oxyde (POM) crystal

The linear and nonlinear optical properties of the 3-methyl-4-nitropyridine-1-oxyde (POM) crystal have been evaluated using semiempirical quantum chemistry techniques. The scheme includes (i) the evaluation of the polarizability and first hyperpolarizability of increasingly large one-dimensional, two-dimensional, and three-dimensional clusters of POM, (ii) the use of the time-dependent Hartree-Fock approach to determine the static and dynamic responses in combination with semiempirical Austin model 1 Hamiltonian, (iii) the assessment, for the POM monomer and dimer, of the electron correlation effects using second-order Moller-Plesset perturbation theory with several basis sets containing polarization and diffuse functions, (iv) the assessment of the validity of the multiplicative scheme and its application to get effective polarizability and first hyperpolarizability of the POM unit cell in the crystal, (v) the use of a sum-over-states approach to attribute the first hyperpolarizability to a dominant charge-transfer excited state, and (vi) comparison with experimental data as well as with calculated values obtained using the oriented gas approximation.     

Modeling the electric field third-order nonlinear responses of an infinite aggregate of hexatriene chains using the electrostatic interaction model

A classical electrostatic polarization scheme using the additive distribution procedure has been applied to determine the static longitudinal polarizability and second hyperpolarizability of a all-trans hexatriene molecule in an infinite stretched fiber. The parameters have been derived from ab initio coupled-perturbed Hartree-Fock calculations and the electrostatic scheme has been validated via comparison with ab initio results on small clusters. Upon packing, the polarizability of all-trans hexatriene increases by 7% whereas the second hyperpolarizability increases by as much as 61%. These increases result from the balance between the enhancement of the (hyper)polarizability due to collinear packing and the reduction associated with lateral packing.     

Numerically stable optimized effective potential method with balanced Gaussian basis sets

A solution to the long-standing problem of developing numerically stable optimized effective potential (OEP) methods based on Gaussian basis sets is presented by introducing an approach consisting of an exact exchange OEP method with an accompanying construction and balancing scheme for the involved auxiliary and orbital Gaussian basis sets that is numerically stable and that properly represents an exact exchange Kohn-Sham method. The method is a purely analytical method that does not require any numerical grid, scales like Hartree-Fock or B3LYP procedures, is straightforward to implement, and is easily generalized to take into account orbital-dependent density functionals other than the exact exchange considered in this work. Thus, the presented OEP approach opens the way to the development and application of novel orbital-dependent exchange-correlation functionals. It is shown that adequately taking into account the continuum part of the Kohn-Sham orbital spectrum is crucial for numerically stable Gaussian basis set OEP methods. Moreover, it is mandatory to employ orbital basis sets that are converged with respect to the used auxiliary basis representing the exchange potential. OEP calculations in the past often did not meet the latter requirement and therefore may have led to erroneously low total energies.     

On the accuracy of density functionals and their basis set dependence: An extensive study on the main group homonuclear diatomic molecules Li2 to Br2

The equilibrium bond distances, harmonic frequencies, and bond dissociation energies of the 21 homonuclear diatomics Li₂—F₂, Na₂—Cl₂, and K₂—Br₂ have been determined using approximate density functional theory (DFT) employing various widely used functionals and basis sets ranging from single zeta to triple zeta plus polarization quality. The results are in general much less sensitive to the size of the basis set as in conventional ab initio molecular orbital (MO) theory, while the choice of the functional is of much more significance. For one basis set (6-311G*), the performance of the DFT-based calculations has been compared and found to be superior to Hartree-Fock (HF) Møller Plesset second order perturbation theory (MP2), or configuration interaction with single and double excitations (CISD) calculations. Particularly, no pathological cases, such as the group 2 dimers (Be₂, Mg₂, Ca₂), are observed. © 1995 by John Wiley & Sons, Inc.     

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

A set of exchange‐correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM‐B3LYP, LC‐BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all‐trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller–Plesset second‐order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM‐B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity‐dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro‐optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field‐induced second harmonic generation all of them, as well as the Hartree–Fock approximation, yield the wrong sign. We have also found that the Pople 6–31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry. © 2013 Wiley Periodicals, Inc.     

Lagrangian approach to molecular vibrational Raman intensities using time-dependent hybrid density functional theory

The authors propose a new route to vibrational Raman intensities based on analytical derivatives of a fully variational polarizability Lagrangian. The Lagrangian is constructed to recover the negative frequency-dependent polarizability of time-dependent Hartree-Fock or adiabatic (hybrid) density functional theory at its stationary point. By virtue of the variational principle, first-order polarizability derivatives can be computed without using derivative molecular orbital coefficients. As a result, the intensities of all Raman-active modes within the double harmonic approximation are obtained at approximately the same cost as the frequency-dependent polarizability itself. This corresponds to a reduction of the scaling of computational expense by one power of the system size compared to a force constant calculation and to previous implementations. Since the Raman intensity calculation is independent of the harmonic force constant calculation more, computationally demanding density functionals or basis sets may be used to compute the polarizability gradient without much affecting the total time required to compute a Raman spectrum. As illustrated for fullerene C60, the present approach considerably extends the domain of molecular vibrational Raman calculations at the (hybrid) density functional level. The accuracy of absolute and relative Raman intensities of benzene obtained using the PBE0 hybrid functional is assessed by comparison with experiment.     

Molecular (hyper)polarizabilities computed by pseudospectral methods

We have developed algorithms based on pseudospectral (PS) ab initio electronic structure methods for solving the first- and second-order Hartree-Fock/Kohn-Sham equations and evaluating molecular polarizabilities and first- and second-order hyperpolarizabilities in the spin-restricted and spin-unrestricted formalisms at the Hartree-Fock (HF) and density functional theory (DFT) levels. We carry out calculations on 50 small molecules to test the accuracy of the PS approach. Our results demonstrate that the molecular polarizability alpha computed by the PS method is essentially identical to the value obtained from conventional methods for both HF and DFT calculations, while the first-order hyperpolarizability beta and second-order hyperpolarizability gamma have mean unsigned percentage differences of 1.26% and 0.62% (HF) and 0.78% and 0.65% (DFT), respectively. We also present CPU timing comparisons between the PS and conventional methods at the 6-31 G(**) level for 14 molecules having 185 to 1185 basis functions. The timing results show that the PS method is 25 (PS-HF) and 13 (PS-DFT) times faster than the conventional method for a system with 500 basis functions. The PS methods are found scale as N(2.70) (PS-HF) and N(2.40) (PS-DFT), while the conventional methods scale as N(2.93) (PRISM-HF) and N(2.87) (PRISM-DFT), where N is the number of basis functions.     

Ab initio determination of the electric multipole moments and static (hyper)polarizability of HCCX,X = F,Cl, Br,and I

We report electric multipole moments and (hyper)polarizabilities for the haloethynes HCCX, X = F, Cl, Br, and I. The molecular properties have been obtained from finite-field self-consistent field, M?ller-Plesset perturbation theory and coupled cluster calculations with large, carefully optimized basis sets of gaussian-type functions. The mean dipole (hyper)polarizability and the mean quadrupole polarizability near the Hartree-Fock limit are alpha/e(2)a(0) (2)E(h) (-1) = 23.74 (HCCF), 37.26 (HCCCl), 43.97 (HCCBr), 56.44 (HCCI), beta/e(3)a(0) (3)E(h) (-2) = -73.9 (HCCF), -67.0 (HCCCl), -39.5 (HCCBr), 42.7 (HCCI), gamma/e(4)a(0) (4)E(h) (-3) = 4,914 (HCCF), 6,554 (HCCCl), 9,328 (HCCBr), 14,949 (HCCI), and C/e(2)a(0) (4)E(h) (-1) = 160.3 (HCCF), 317.1 (HCCCl), 471.2 (HCCBr), 671.2 (HCCI). Electron correlation has a small effect on the dipole polarizability but affects strongly the hyperpolarizability. Agreement with the available experimental data is more or less fair for HCCF, HCCCl, and HCCBr but less satisfactory for HCCI.     

呋喃同系物C4H4X(X=O,S,Se,Te)非线性光学性质的TDDFT-SOS理论研究

用含时密度泛函理论(TD-DFT)组合态求和(SOS)方法计算了呋喃同系物[呋喃(C4H4O)、噻吩(C4H4S)、硒吩(C4H4Se)、碲吩(C4H4Te)]的非线性光学性质.计算结果表明,体系的三阶NLO系数(γ)随着杂原子被重原子的取代而逐步增大,B3LYP等4种势函数计算的NLO系数基本一致.计算的色散关系曲线表明,标题化合物在宽频区存在小的色散作用,是一类具有应用前景的NLO材料.