Theoretical study of the longitudinal first hyperpolarizability of polysilaacetylene

With the help of ab initio tools taking into account dynamic electron correlation effects, we study the longitudinal electronic first hyperpolarizability of carbon-silicon analogues to polyacetylene. It turns out that the MP2/6-31G(d)//HF/6-31G(d) scheme is suitable to obtain a semiquantitative accuracy for the first hyperpolarizability of long polysilaacetylene oligomers. The conformation of the chain has a crucial impact on its second-order nonlinear optical properties. We also show that, for some chain lengths, the frequency dispersion effects may have a huge impact, even when far away from resonance. These phenomena are rationalized in terms of delocalization and asymmetry.     

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.     

Estimates of the structure and dimerization energy of polyacetylene from ab initio calculations on finite polyenes

Ab initio calculations at the Hartree-Fock (HF) and the second-order Møller-Plesset (MP2) levels are performed for finite polyenes C_2nH_2n+2 to estimate the structure and dimerization energy (E_dim) of polyacetylene. The effect of electron correlation on the structure of finite polyenes is analyzed in detail. The MP3/6–31G* C(DOUBLE BOND)C and C(SINGLE BOND)C bond lengths in polyacetylene are estimated by a simple extrapolation method using empirical corrections for the MP2 deficiencies, yielding values [C(DOUBLE BOND)C(MP3) ∼ 1.36 Å and C(SINGLE BOND)C(MP3) ∼ 1.44 Å] that are in a good agreement with experiment (C(DOUBLE BOND)C (DOUBLE BOND) 1.36 Å and C(SINGLE BOND)C (DOUBLE BOND) 1.44–1.45 Å). Comparison is also made with other theoretical estimates of polyacetylene structure. E_dim is approximated by the energy difference between the equilibrium and hypothetical polyenic structures. It is estimated that E_dim is ∼ 1.4–1.5 kcal/mol (0.06–0.07 eV) per carbon-carbon bond at the HF level with 4–21G and 6–31G* basis sets and ∼ 0.3–0.5 kcal/mol (0.013–0.022 eV) at the MP2 level with the 6–31G* basis set. It is concluded that E_dim is very sensitive to the level of approximation employed so that a proper treatment of electron correlation is essential to obtain a reliable estimate of the dimerization energy. © 1997 John Wiley & Sons, Inc.     

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.     

First hyperpolarizability of polymethineimine with long-range corrected functionals

Using the long-range corrected (LC) density functional theory (DFT) scheme introduced by Iikura et al. [J. Chem. Phys. 115, 3540 (2001)] and the Coulomb-attenuating model (CAM-B3LYP) of Yanai et al. [Chem. Phys. Lett. 393, 51 (2004)], we have calculated the longitudinal dipole moments and static electronic first hyperpolarizabilities of increasingly long polymehtineimine oligomers. For comparison purposes Hartree-Fock (HF), Moller-Plesset perturbation theory (MP2), and conventional pure and hybrid functionals have been considered as well. HF, generalized gradient approximation (GGA), and conventional hybrids provide too large dipole moments for long oligomers, while LC-DFT allows to reduce the discrepancy with respect to MP2 by a factor of 3. For the first hyperpolarizability, the incorrect evolution with the chain length predicted by HF is strongly worsened by BLYP, Perdew-Burke-Ernzerhof (PBE), and also by B3LYP and PBE0. On the reverse, LC-BLYP and LC-PBE hyperpolarizabilities are correctly predicted to be positive (but for the two smallest chains). Indeed, for medium and long oligomers LC hyperpolarizabilities are slightly smaller than MP2 hyperpolarizabilities, as it should be. CAM-B3LYP also strongly improves the B3LYP results, though a bit less impressively for small chain lengths. The present study demonstrates the efficiency of long-range DFT, even in very pathological cases.     

Electron-correlated calculations of the nuclear-shielding polarizability and magnetizability polarizability of H2, N2, HF, and CO

The effects of a uniform static electric field on the NMR shielding and magnetizability of H₂, N₂, HF, and CO are reported. The appropriate defining quantities are the shielding and magnetizability polarizabilities and these are calculated in a mixed numeric-analytic scheme with allowance for electron correlation via third-order Møller-Plesset (MP3) theory or linearized coupled cluster double excitation (L-CCD) theory. This is the first time that these theories have been applied to these properties. Our primary conclusion for the shielding polarizabilities is that, with the exception of H₂, the use of coupled cluster theory is necessary to establish the definitive values for these properties because of their extreme sensitivity to electron correlation. For the magnetizability polarizabilities we find the MP3 values to be in better agreement with the L-CCD results than the MP2 values are.     

Effects of an electric field on interaction of aromatic systems

The effect of uniform external electric field on the interactions between small aromatic compounds and an argon atom is investigated using post‐HF (MP2, SCS‐MP2, and CCSD(T)) and density functional (PBE0‐D3, PBE0‐TS, and vdW‐DF2) methods. The electric field effect is quantified by the difference of interaction energy calculated in the presence and absence of the electric field. All the post‐HF methods describe electric field effects accurately although the interaction energy itself is overestimated by MP2. The electric field effect is explained by classical electrostatic models, where the permanent dipole moment from mutual polarization mainly determines its sign. The size of π‐conjugated system does not have significant effect on the electric field dependence. We found out that PBE0‐based methods give reasonable interaction energies and electric field response in every case, while vdW‐DF2 sometimes shows spurious artifact owing to its sensitivity toward the real space electron density. © 2015 Wiley Periodicals, Inc.     

Improved accuracy with medium cost computational methods for the evaluation of bond length alternation of increasingly long oligoacetylenes

The difference between the length of the central carbon-carbon bond and that of the adjacent flanked double bonds in polymers such as polyacetylene is closely related to their electronic properties and plays a central role in their conductivity upon doping. Simple as it seems, this bond length alternation (BLA) is a difficult test for many theoretical methods. Accurate coupled-cluster (CC) benchmark values are difficult to obtain even for small- and medium-sized oligoacetylenes due to their intrinsic computational limitations. Here we present a computationally much cheaper alternative to obtain accurate benchmark BLA values, even for large polyacetylene oligomers, by using the so-called spin-component scaled M?ller-Plesset perturbation theory up to second order (SCS-MP2). Comparison between these new benchmark BLA with those provided by density functional theory (DFT) calculations shows a large dispersion of the results depending on the amount of exact exchange used in the exchange-correlation functional. We find that the percentage of exact exchange needed to accurately reproduce the new benchmark BLA is much larger than previously thought when comparison was made with values obtained using the MP2 method.     

The effective fragment potential: small clusters and radial distribution functions

The effective fragment potential (EFP) method for treating solvent effects provides relative energies and structures that are in excellent agreement with the analogous fully quantum [i.e., Hartree-Fock (HF), density functional theory (DFT), and second order perturbation theory (MP2)] results for small water clusters. The ability of the method to predict bulk water properties with a comparable accuracy is assessed by performing EFP molecular dynamics simulations. The resulting radial distribution functions (RDF) suggest that as the underlying quantum method is improved from HF to DFT to MP2, the agreement with the experimental RDF also improves. The MP2-based EFP method yields a RDF that is in excellent agreement with experiment.     

Revisiting the relationship between the bond length alternation and the first hyperpolarizability with range-separated hybrid functionals

We monitor the influence of the bond length alternation (BLA) modification on the static electronic polarizability and first hyperpolarizability of two polymethineimine oligomers. Four theoretical approaches are compared: HF, PBE0, LC-omegaPBE, and MP2. For the dodecamer, both HF and PBE0 are unable to foresee even the qualitative evolution of the first hyperpolarizability when varying the BLA. On the contrary, LC-omegaPBE provides (non)linear optics properties in agreement with MP2 results, especially for the longer chains. This confirms the interest of range-separated hybrids for the computation of the (hyper)polarizabilities of extended pi-conjugated compounds.     

Ab initio quantum chemical calculation of electron density,electrostatic potential,and electric field of biomolecule based on fragment molecular orbital method

Efficient quantum chemical calculations of electrostatic properties, namely, the electron density (EDN), electrostatic potential (ESP), and electric field (EFL), were performed using the fragment molecular orbital (FMO) method. The numerical errors associated with the FMO scheme were examined at the HF, MP2, and RI‐MP2 levels of theory using 4 small peptides. As a result, the FMO errors in the EDN, ESP, and EFL were significantly smaller than the magnitude of the electron correlation effects, which indicated that the FMO method provides sufficiently accurate values of electrostatic properties. In addition, an attempt to reduce the computational effort was proposed by combining the FMO scheme and a point charge approximation. The error due to this approximation was examined using 2 proteins, prion protein and human immunodeficiency virus type 1 protease. As illustrative examples, the ESP values at the molecular surface of these proteins were calculated at the MP2 level of theory.     

Structure and ultrafast dynamics of liquid water: a quantum mechanics/molecular mechanics molecular dynamics simulations study

A quantum mechanics/molecular mechanics molecular dynamics simulation was performed for liquid water to investigate structural and dynamical properties of this peculiar liquid. The most important region containing a central reference molecule and all nearest surrounding molecules (first coordination shell) was treated by Hartree-Fock (HF), post-Hartree-Fock [second-order Moller-Plesset perturbation theory (MP2)], and hybrid density functional B3LYP [Becke's three parameter functional (B3) with the correlation functional of Lee, Yang, and Parr (LYP)] methods. In addition, another HF-level simulation (2HF) included the full second coordination shell. Site to site interactions between oxygen-oxygen, oxygen-hydrogen, and hydrogen-hydrogen atoms of all ab initio methods were compared to experimental data. The absence of a second peak and the appearance of a shoulder instead in the gO-O graph obtained from the 2HF simulation is notable, as this feature has been observed so far only for pressurized or heated water. Dynamical data show that the 2HF procedure compensates some of the deficiency of the HF one-shell simulation, reducing the difference between correlated (MP2) and HF results. B3LYP apparently leads to too rigid structures and thus to an artificial slow down of the dynamics.     

Two-step evaluation of binding energy and potential energy surface of van der Waals complexes

Evaluation of intermolecular distance and binding energy (BE) of van der Waals complex/cluster at ab initio level of theory is computationally demanding when many monomers are involved. Starting from MP2 energy, we reached a two-step evaluation method of BE of van der Waals complex/cluster through reasonable approximations; BE = BE(HF) + sum Mi> Mj{BE (Mi- Mj)(MP2 or MP2.5) - BE(Mi-Mj)(HF)} where HF represents the Hartree-Fock calculation, Mi, Mj, etc. are interacting monomers, and MP2.5 represents the arithmetic mean of MP2 and MP3. The first term is the usual BE of the complex/cluster evaluated at the HF level. The second term is the sum of the difference in two-body BE between the correlated and HF levels of theory. This equation was applied to various van der Waals complexes consisting of up-to-four monomers at MP2 and MP2.5 levels of theory. We found that this method is capable of providing precise estimate of the BE and reproducing well the potential energy surface of van der Waals complexes/clusters; the maximum error of the BE is less than 1 kcal/mol and 1% in most cases except for several limited cases. The origins of error in these cases are discussed in detail.     

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.     

Electronic structure and spectroscopic properties of the two structural isomers of donor-acceptor substituted sesquifulvalene in the gas and solution phases-a case study of sudden polarization

The ground state equilibrium structure and electric properties of two structural isomers of donor-acceptor substituted sesquifulvalene have been calculated at ab initio HF and MP2 levels for different conformations. The electronic properties of low lying excited singlets are calculated by using CI calculations including single excitations only. Isomer I in which the inter-ring charge transfer (CT) is reinforced in the presence of substituents shows sudden polarization in the ground and two lower lying excited states, while isomer II in which the longitudinal CT interaction is attenuated does not exhibit sudden polarization. The phenomenon of sudden polarization has been rationalized in terms of the easy polarization, smaller rotational barrier, and enhanced inter-ring CT on going from the planar to the orthogonal geometry. The appreciably large static second-order polarizability of I stems from its sudden polarized ground state. The solvent (using the conductor-like polarizable continuum model (CPCM)) plays a significant role on the modulation of ground and excited state electronic properties which, in general, predicts blue-shifts for I. However, for molecule II, the two lower energy transitions show a red-shift while the others show a weaker blue-shift at any conformation.     

On the effect of electron correlation on the static second hyperpolarizability of π conjugated oligomer chains

In this article, we report on the ab initio calculation of the static longitudinal second hyperpolarizability (γ) of π conjugated unsaturated oligomer chains using polyacetylene and polyyne as model compounds. The common observation is that the electron correlation enhances γ in these systems. The present study reveals that for extended chain lengths the opposite appears to be true: Electron correlation may have a damping effect on this property. For double-zeta basis sets, a negative contribution from electron correlation to γ is found within the range of chain lengths investigated. For triple-zeta basis sets, the same behavior must be anticipated at larger chain lengths based on extrapolation schemes. The analysis of the excitation energies and transition moments shows that transition moments between excited states as predicted by the Hartree-Fock and coupled cluster methods have a different response to chain length extension. There also are indications that higher order correlation effects will enhance γ.     

适用于液晶大分子的量子化学计算方法以及六烷氧基苯并菲取代的1,3,5-三酰胺苯液晶的研究

盘状液晶分子之间的相互作用决定液晶的性质. 为了选择合适的计算方法, 以便用量子化学研究液晶大分子, 设计了对位取代苯和三酰胺苯作为模型分子, 用高水平的ONIOM [MP2/6-31G*(0.25):HF/6-31G(d,p)]计算提供了与晶体结构资料相符合的较准确的二体相互作用结果. 然后与各种较低级别的计算进行比较, 说明ONIOM (HF/STO-3G: AM1:UFF)水平比较合适. 盘重叠部分的相互作用主要是色散作用, 用UFF力场处理, 氢键主要是静电作用, 用HF/STO-3G处理, 其余部分用AM1处理. 通过对苯取代的1,3,5-三酰胺苯的双分子构型优化, 并与晶体结构数据进行比较, 进一步说明ONIOM (HF/STO-3G:AM1:UFF)水平计算的适用性. 在此基础上, 对六烷氧基苯并菲取代的1,3,5-三酰胺苯的双分子构型进行了优化, 为解释它所形成的液晶具有较高的电荷传输能力提供了有用的信息.     

Ab initio investigation of water clusters (H2O)n (n = 2–34)

Various properties of typical structures of water clusters in the n = 2–34 size regime with the change of cluster size have been systematically explored. Full optimizations are carried out for the structures presented in this article at the Hartree–Fock (HF) level using the 6‐31G(d) basis set by taking into account the positions of all atoms within the cluster. The influence of the HF level on the results has been reflected by the comparison between the binding energies of (H₂O)_n (n = 2–6, 8, 11, 13, 20) calculated at the HF level and those obtained from high‐level ab initio calculations at the second‐order Møller–Plesset (MP2) perturbation theory and the coupled cluster method including singles and doubles with perturbative triples (CCSD(T)) levels. HF is inaccurate when compared with MP2 and CCSD(T), but it is more practical and allows us to study larger systems. The computed properties characterizing water clusters (H₂O)_n (n = 2–34) include optimal structures, structural parameters, binding energies, hydrogen bonds, charge distributions, dipole moments, and so on. When the cluster size increases, trends of the above various properties have been presented to provide important reference for understanding and describing the nature of the hydrogen bond. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

A comparison of Hartree—Fock,MP2, and DFT results for the HCN dimer and crystal

A number of hydrogen-bond related quantities—geometries, interaction energies, dipole moments, dipole moment derivatives, and harmonic vibrational frequencies—were calculated at the Hartree—Fock, MP2, and different DFT levels for the HCN dimer and the periodic HCN crystal. The crystal calculations were performed with the Hartree—Fock program CRYSTAL92, which routinely allows an a posteriori electron-correlation correction of the Hartree—Fock obtained lattice energy using different correlation-only functionals. Here, we have gone beyond this procedure by also calculating the electron-correlation energy correction during the structure optimization, i.e., after each CRYSTAL92 Hartree—Fock energy evaluation, the a posteriori density functional scheme was applied. In a similar manner, we optimized the crystal structure at the MP2 level, i.e., for each Hartree—Fock CRYSTAL92 energy evaluation, an MP2 correction was performed by summing the MP2 pair contributions from all HCN molecules within a specified cutoff distance. The crystal cell parameters are best reproduced at the Hartree—Fock and the nongradient-corrected HF + LDA and HF + VWN levels. The BSSE-corrected MP2 method and the HF + P91, HF + LDA, and HF + VWN methods give lattice energies in close agreement with the ZPE-corrected experimental lattice energy. The (HCN)₂ dimer properties are best reproduced at the MP2 level, at the gradient-corrected DFT levels, and with the B3LYP and BHHLYP methods. © 1996 John Wiley & Sons, Inc.     

Second-order Møller-Plesset perturbation energy obtained from divide-and-conquer Hartree-Fock density matrix

The density matrix (DM) obtained from Yang's [Phys. Rev. Lett. 66, 1438 (1991)] divide-and-conquer (DC) Hartree-Fock (HF) calculation is applied to the explicit second-order M?ller-Plesset perturbation (MP2) energy functional of the HF DM, which was firstly mentioned by Ayala and Scuseria [J. Chem. Phys. 110, 3660 (1999)] and was improved by Surján [Chem. Phys. Lett. 406, 318 (2005)] as DM-Laplace MP2. This procedure, termed DC-DM MP2, requires the HF DM of holes, for which we propose two evaluation schemes in DC manner. Numerical studies reveal that the DC-DM MP2 energy deviation from canonical MP2 is the same order of magnitude as DC-HF energy deviation from conventional HF whichever type of hole DM is adopted. It is also confirmed that the central processing unit time of DC-DM MP2 is less than that of DM-Laplace MP2 because the DC-HF DM is sparser than conventional DM.