The ORP basis set designed for optical rotation calculations

Details of generation of the optical rotation prediction (ORP) basis set developed for accurate optical rotation (OR) calculations are presented. Specific rotation calculations carried out at the density functional theory (DFT) level for model chiral methane molecule, fluorooxirane, methyloxirane, and dimethylmethylenecyclopropane reveal that the ORP set outperforms larger basis sets, among them the aug‐cc‐pVTZ basis set of Dunning (J. Chem. Phys. 1989, 90, 1007) and the aug‐pc‐2 basis set of Jensen (J. Chem. Phys. 2002, 117, 9234; J. Chem. Theory Comput. 2008, 4, 719). It is shown to be an attractive choice also in the case of larger systems, namely norbornanone, β‐pinene, trans‐pinane, and nopinone. The ORP basis set is further used in OR calculations for 24 other systems, and the results are compared to the aug‐cc‐pVDZ values. Whenever large discrepancies of results are observed, the ORP values are in an excellent agreement with the aug‐cc‐pVTZ results. The ORP basis set enables accurate specific rotation calculations at a reduced cost and thus can be recommended for routine DFT OR calculations, also for large and conformationally flexible molecules. © 2013 Wiley Periodicals, Inc.     

Accurate calculations of dynamic first hyperpolarizability: Construction of physically justified slater‐type basis sets

An efficient procedure for construction of physically rationalized Slater‐type basis sets for calculations of dynamic hyperpolarizability is proposed. Their performance is evaluated for the DFT level calculations for model molecules, carried out with a series of functionals. Advantages of new basis sets over standard d‐aug‐cc‐pVTZ and recently developed LPOL‐(FL,FS) Gaussian‐type basis sets are discussed. © 2014 Wiley Periodicals, Inc.     

Reduced-size polarized basis sets for calculations of molecular electric properties. I. The basis set generation

Following the recent studies of basis sets explicitly dependent on oscillatory external electric field we have investigated the possibility of some further truncation of the so-called polarized basis sets without any major deterioration of the computed data for molecular dipole moments, dipole polarizabilities, and related electric properties of molecules. It has been found that basis sets of contracted Gaussian functions of the form [3s1p] for H and [4s3p1d] for the first-row atoms can satisfy this requirement with particular choice of contractions in their polarization part. With m denoting the number of primitive GTOs in the contracted polarization function, the basis sets devised in this article will be referred to as the ZmPol sets. In comparison with earlier, medium-size polarized basis sets (PolX), these new ZmPol basis sets are reduced by 2/3 in their size and lead to the order of magnitude computing time savings for large molecules. Simultaneously, the dipole moment and polarizability data remain at almost the same level of accuracy as in the case of the PolX sets. Among a variety of possible applications in computational chemistry, the ZmPolX are also to be used for calculations of frequencies and intensities in the Raman spectra of large organic molecules (see Part II, this issue).     

Ab initio calculations of the Ar–ethane intermolecular potential energy surface using bond function basis sets

The intermolecular potential energy surface (PES) of argon with ethane has been studied by ab initio calculations at the levels of second‐order Møller–Plesset perturbation (MP2) theory and coupled‐cluster theory with single, double, and noniterative triple configurations (CCSD(T)) using a series of augmented correlation‐consistent basis sets. Two sets of bond functions, bf1 (3s3p2d) and bf2 (6s6p4d2f), have been added to the basis sets to show a dramatic and systematic improvement in the convergence of the entire PES. The PES of Ar–ethane is characterized by a global minimum at a near T‐shaped configuration with a well depth of 0.611 kcal mol^?1, a second minimum at a collinear configuration with a well depth of 0.456 kcal mol^?1, and a saddle point connecting the two minima. It is shown that an augmented correlation‐consistent basis set with a set of bond functions, either bf1 or bf2, can effectively produce results equivalent to the next larger augmented correlation‐consistent basis set, that is, aug‐cc‐pVDZ‐bf1 ≈ aug‐cc‐pVTZ, aug‐cc‐pVTZ‐bf1 ≈ aug‐cc‐pVQZ. Very importantly, the use of bond functions improves the PES globally, resulting accurate potential anisotropy. Finally, MP2 method is inadequate for accurate calculations, because it gives a potentially overestimated well depth and, more seriously, a poor potential anisotropy. © 2012 Wiley Periodicals, Inc.     

Basis sets for the evaluation of van der Waals complex interaction energies: Ne–N2 intermolecular potential and microwave spectrum

In order to obtain efficient basis sets for the evaluation of van der Waals complex intermolecular potentials, we carry out systematic basis set studies. For this, interaction energies at representative geometries on the potential energy surfaces are evaluated using the CCSD(T) correlation method and large polarized LPol‐n and augmented polarization‐consistent aug‐pc‐2 basis sets extended with different sets of midbond functions. On the basis of the root mean square errors calculated with respect to the values for the most accurate potentials available, basis sets are selected for fitting the corresponding interaction energies and getting analytical potentials. In this work, we study the Ne–N₂ van der Waals complex and after the above procedure, the aug‐pc‐2–3321 and the LPol‐ds‐33221 basis set results are fitted. The obtained potentials are characterized by T‐shaped global minima at distances between the Ne atom and the N₂ center of mass of 3.39 Å, with interaction energies of ?49.36 cm^?1 for the aug‐pc‐2–3321 surface and ?50.28 cm^?1 for the LPol‐ds‐33221 surface. Both sets of results are in excellent agreement with the reference surface. To check the potentials further microwave transition frequencies are calculated that agree well with the experimental and the aV5Z‐33221 values. The success of this study suggests that it is feasible to carry out similar accurate calculations of interaction energies and ro‐vibrational spectra at reduced cost for larger complexes than has been possible hitherto. © 2013 Wiley Periodicals, Inc.     

On the performance of long‐range‐corrected density functional theory and reduced‐size polarized LPol‐n basis sets in computations of electric dipole (hyper)polarizabilities of π‐conjugated molecules

Static longitudinal electric dipole (hyper)polarizabilities are calculated for six medium‐sized π‐conjugated organic molecules using recently developed LPol‐n basis set family to assess their performance. Dunning's correlation‐consistent basis sets of triple‐ζ quality combined with MP2 method and supported by CCSD(T)/aug‐cc‐pVDZ results are used to obtain the reference values of analyzed properties. The same reference is used to analyze (hyper)polarizabilities predicted by selected exchange‐correlation functionals, particularly those asymptotically corrected. © 2012 Wiley Periodicals, Inc.     

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.     

Ab initio dipole polarizability surfaces of water molecule: static and dynamic at 514.5 nm

Coupled cluster calculations with a carefully designed basis set have been performed to obtain both static, alpha, and dynamic at 514.5 nm, alpha(514.5 nm), dipole polarizability surfaces of water. We employed a medium size basis set (13s10p6d3f9s6p2d1f)[9s7p6d3f6s5p2d1f] consisting of 157 contracted Gaussian-type functions that yields values near the Hartree-Fock limit for alpha [G. Maroulis, J. Chem. Phys. 94, 1182 (1991)]. The alpha and alpha(514.5 nm) surfaces were able to reproduce all the experimentally available information about the dipole polarizability of water, especially the Raman spectra of gaseous H(2)O, D(2)O, and HDO. Vibrational averages for the dipole polarizability of water molecule are also reported.     

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.     

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.     

Spin‐orbit ZORA and four‐component Dirac–Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers

Hartree–Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange‐correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin‐orbit zeroth‐order regular approximation Hamiltonian in combination with the large Slater‐type basis set QZ4P as well as with the four‐component Dirac–Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization‐consistent basis sets aug‐pcSseg‐4 for He, Ne and Ar, aug‐pcSseg‐3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero‐point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.     

Model studies of the optical rotation,and theoretical determination of its sign for β‐pinene and trans‐pinane

We have carried out extensive studies on the basis set dependence of the calculated specific optical rotation (OR) in molecules at the level of the time–dependent Hartree–Fock and density functional approximations. To reach the limits of the basis set saturation, we have devised an artificial model, the asymmetrically deformed (chiral) methane (CM) molecule. This small system permits to use basis sets which are prohibitively large for real chiral molecules and yet shows all the important features of the basis set dependence of the OR values. The convergence of the OR has been studied with n‐aug‐cc‐pVXZ basis sets of Dunning up to the 6–ζ. In a parallel series of calculations, we have used the recently developed large polarized (LPolX) basis sets. The relatively small LPolX sets have been shown to be competitive to very large n‐aug‐cc‐pVXZ basis sets. The conclusions reached in calculations of OR in CM concerning the usefulness of LPolX basis sets have been further tested on (S)‐methyloxirane and (S)‐fluoro‐oxirane. The smallest set of the LPolX family (LPol–ds) has been found to yield OR values of similar quality as those obtained with much larger Dunning's aug‐cc‐pVQZ basis set. These results have encouraged us to carry out the OR calculations with LPol–ds basis sets for systems as large as β‐pinene and trans‐pinane. In both cases, our calculations have lead to the correct sign of the OR value in these molecules. This makes the relatively small LPol–ds basis sets likely to be useful in OR calculations for large molecules. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

Basis set convergence of explicitly correlated double-hybrid density functional theory calculations

The basis set convergence of explicitly correlated double-hybrid density functional theory (DFT) is investigated using the B2GP-PLYP functional. As reference values, we use basis set limit B2GP-PLYP-F12 reaction energies extrapolated from the aug(')-cc-pV(Q+d)Z and aug(')-cc-pV(5+d)Z basis sets. Explicitly correlated double-hybrid DFT calculations converge significantly faster to the basis set limit than conventional calculations done with basis sets saturated up to the same angular momentum (typically, one "gains" one angular momentum in the explicitly correlated calculations). In explicitly correlated F12 calculations the VnZ-F12 basis sets converge faster than the orbital A(')VnZ basis sets. Furthermore, basis set convergence of the MP2-F12 component is apparently faster than that of the underlying Kohn-Sham calculation. Therefore, the most cost-effective approach consists of combining the MP2-F12 correlation energy from a comparatively small basis set such as VDZ-F12 with a DFT energy from a larger basis set such as aug(')-cc-pV(T+d)Z.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The basis set polarization approach is employed for the generation of medium-size polarized GTO/CGTO basis sets for calculations of molecular dipole moments and polarizabilities. The excellent performance of the [13.10.4/7.5.2] GTO/CGTO polarized basis sets derived for Si through Cl is illustrated by the atomic polarizability results and SCF and MBPT data for dipole moments and polarizabilities of the second-row atom hydrides. The possible applications of the electric-property oriented polarized basis sets are discussed. The basis set data for Si through Cl are those for H and C through F append the paper.     

Au的乙炔配合物非线性光学性质的量子化学计算

对过渡金属Au的有机配合物Ph3PAuC≡CR (R＝C6H4OCH3, Ph, C6H4NO2和PyNO2)的极化率和一阶、二阶超极化率进行了量子化学计算. 构型在B3LYP/CEP-121G水平优化. 用有效模型势方法和二阶多体微扰方法分别考虑了相对论效应和电子相关效应. 对基组进行了慎重的选择, 以ECP-HYPOL基组为对照标准, 在LFK基组基础上简化得到一个较小的基组LFK2. 计算结果与实测结果趋势一致.     

Comparison of ground and excited state polarizabilities of thiophene,cyclopentadiene, and fulvene oligomers and their cyano substituted derivatives—Ab initio study

Ab Initio study of the ground and excited state polarizabilities of thiophene, fulvene, and cyclopentadiene based conducting oligomers and their cyano derivatives have been performed using the restricted Hartree–Fock (RHF) and the configuration interaction singles (CIS) approaches, respectively, with 3‐21G* basis set. For comparison purposes, for some small oligomers (monomers and dimers), higher basis sets (6‐31G*, 6‐31+G*, aug‐cc‐pVTZ) were also employed in the computations of polarizabilities. The trends in polarizability as a function of oligomer length were investigated. For all systems, the RHF polarizability increases as n^1.2–1.3 as n gets larger and the CIS polarizability increases as n^1.4–1.6 for n less than seven or eight rings and then increases approximately linearly with n for larger n. For the thiophene based systems the dependence of the polarizability on bond length alternation (BLA) along the backbone of the oligomers was also investigated using the RHF, density functional (DFT), and CIS theories (with 3‐21G* basis set). For thiophene dimer, we also performed RHF/aug‐cc‐pVTZ calculations of polarizabilities versus BLA. We found that the polarizability is largest when BLA is near zero (for both ground and excited states), which correlates with the lowest excitation energy. Comparison with experimental results has been made where possible. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1983–1995, 2007