Accurate atomic Gaussian basis functions for second-row atoms: Small split-valence 3-21SP and 4-22SP basis sets

Small split-valence Gaussian 3-21SP and 4-22SP basis sets, previously reported for the first-row atoms [Chem. Phys. Lett., 229 , 151 (1996)], have been extended for the second-row elements of the Periodic Table. The total energies of the ground states of the second-row atoms calculated with the new basis sets are significantly lower than those obtained with the well-known 3-21G (J. Am. Chem. Soc., 104 , 2797 (1982)] and 4-31G [J. Chem. Phys., 56 , 5255 (1972)] basis sets. This is because, as first noted in our previous work for first-row atoms, that the 3-21G and 4-31G basis sets only correspond to a local minimum of the Hartree–Fock energy functional, which is relatively far from its global minimum. The proposed basis sets have been tested by performing geometry optimizations and calculations of normal frequencies in the harmonic approximation of some diatomic and polyatomic molecules at the Hartree–Fock level. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1200–1210     

An improved generator coordinate Hartree–Fock method applied to the choice of contracted Gaussian basis sets for first‐row diatomic molecules

Accurate Gaussian basis sets (18s for Li and Be and 20s11p for the atoms from B to Ne) for the first‐row atoms, generated with an improved generator coordinate Hartree–Fock method, were contracted and enriched with polarization functions. These basis sets were tested for B₂, C₂, BeO, CN⁻, LiF, N₂, CO, BF, NO⁺, O₂, and F₂. At the Hartree–Fock (HP), second‐order Møller–Plesset (MP2), fourth‐order Møller–Plesset (MP4), and density functional theory (DFT) levels, the dipole moments, bond lengths, and harmonic vibrational frequencies were studied, and at the MP2, MP4, and DFT levels, the dissociation energies were evaluated and compared with the corresponding experimental values and with values obtained using other contracted Gaussian basis sets and numerical HF calculations. For all diatomic molecules studied, the differences between our total energies, obtained with the largest contracted basis set [6s5p3d1f], and those calculated with the numerical HF methods were always less than 3.2 mhartree. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 15–23, 2000     

H2O,H2, HF,F2 and F2O nuclear magnetic shielding constants and indirect nuclear spin–spin coupling constants (SSCCs) in the BHandH/pcJ‐n and BHandH/XZP Kohn–Sham limits

Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H₂O, H₂, HF, F₂ and F₂O nuclear isotropic shielding constants in the BHandH Kohn–Sham basis set limit was shown. The results of two‐ and three‐parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization‐consistent basis sets pcS‐n and pcJ‐n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were more sensitive to the XZP basis set size and generally less accurate than those estimated using pcJ‐n basis set family. The BHandH density functional markedly outperforms B3LYP method in predicting heavy atom shieldings and SSCCs values in the studied systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Can STO basis sets do a good job in evaluating molecular electromagnetic properties? I. First hyperpolarizability of H2O, CH4, and NH3 according to the TDHF theory

The performance of STO basis sets for the ab initio estimation of the nonlinear electromagnetic response properties of molecules, in terms of a time-dependent Hartree–Fock procedure, is investigated. Applications to the case of the first dynamic hyperpolarizability of three simple polyatomics (H₂O, CH₄, NH₃) adopting several extended basis sets are reported and discussed. Independent estimates for the observables investigated obtained by the same approach in terms of Gaussian basis sets are confronted with our findings in the search for recipes of possible utility.Acknowledgements This research has been partially supported by funds provided by the Italian Consiglio Nazionale delle Ricerche (contribution n. CTB 00.00650.PF34) and Pisa University (fondi di Ateneo, ex 60%, years 2001–2002).Contribution to the Jacopo Tomasi Honorary Issue     

HF and MP2 calculations on CN−, N2, AlF,SiO, PN,SC, ClB,and P2 using correlated molecular wave functions

Contracted basis sets of double zeta valence quality plus polarization functions (DZP) and augmented DZP basis sets, which were recently constructed for the first‐ and second‐row atoms, are applied to study the electronic ground states of the diatomic molecules CN^?, N₂, AlF, SiO, PN, SC, ClB, and P₂. At the Hartree–Fock (HF) and/or Møller–Plesset second‐order (MP2) levels, total and molecular orbital energies, dissociation energies, bond lengths, harmonic vibrational frequencies, and dipole moments are calculated and compared with available experimental data and with the results obtained from correlation consistent polarized valence basis sets of Dunning's group. For N₂, calculations of polarizabilities at the HF and MP2 levels with the sets presented above are also done and compared with results reported in the literature. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

New basis sets for the evaluation of interaction‐induced electric properties in hydrogen‐bonded complexes

Interaction‐induced static electric properties, that is, dipole moment, polarizability, and first hyperpolarizability, of the CO? (HF)_n and N₂? (HF)_n, n = 1–9 hydrogen‐bonded complexes are evaluated within the finite field approach using the Hartree–Fock, density functional theory, Møller–Plesset second‐order perturbation theory, and coupled cluster methods, and the LPol‐n (n = ds, dl, fs, fl) basis sets. To compare the performance of the different methods with respect to the increase of the complex size, we consider as model systems linear chains of the complexes. We analyze the results in terms of the many‐body and cooperative effects. © 2012 Wiley Periodicals, Inc.     

Compton profiles and polarizability as two similar probes of the electronic structure of 14 electron diatomic molecules: An ab initio study

High‐ and low‐energy scattering properties, namely, Compton profiles and polarizability, respectively, were calculated at the configuration interaction (CI) level from molecular orbitals expressed in the linear combination of atomic orbitals (LCAO) model for 14 electron diatomic molecules. Extended atomic basis sets including about 100 Gaussian‐type functions (GTFs) were used. The isotropic and directional Compton profiles and the polarizability show that the behavior of CO and N₂ is rather similar but very different from that of BF. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 63–74, 1999     

2‐Amino derivatives of 5‐nitro­phenyl­acet­amide

The structures of the potential non‐linear optical (NLO) materials N‐[2‐(iso­propyl­amino)‐5‐nitro­phenyl]­acet­amide, (I) C₁₁H₁₅N₃O₃, and N‐[2‐(butyl­amino)‐5‐nitro­phenyl]­acet­amide, (II) C₁₂H₁₇N₃O₃, have been investigated by X‐ray analysis. To compare them with the structure of N‐[2‐(di­methyl­amino)‐5‐nitro­phenyl]­acet­amide, (III) C₁₀H₁₃N₃O₃, a known NLO compound, we had to redetermine the structure of (III), since it was described only briefly in the literature. There are two mol­ecules in the asymmetric unit of compound (I), which have different orientations of the substituents with respect to the benzene ring. The packing of mol­ecules in (II) and (III) contains stacks but both (I) and (II) crystallize in a centrosymmetric space group, which renders them inappropriate for NLO applications.     

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     

A reassessment of some restricted Hartree–Fock limit molecular energies and an investigation of the applicability of Ermler and Kern's procedure for their estimation

New estimates of Hartree–Fock limit energies (E_RHF) for selected AH and AH_n hydrides, diatomic and linear polyatomic molecules have been made utilizing E_SCF values recently reported in the literature for HF, N₂, CO, NH₃, and CH₄ which are very close to the respective limits. These new values have been used to investigate the applicability of Ermler and Kern's procedure for estimating E_RHF: i.e., a factor f is first evaluated from data for reference molecules, where f = E_RHF/E_SCF, which is then used with E_SCF values for other molecules to obtain their E_RHF values. f has been evaluated for three groups of reference molecules? HF, H₂O, NH₃, CH₄, N₂, and CO; CH₄, C₂H₂, C₂H₄, and C₂H₆; and C₂H₂, HCN, and N₂? utilizing E_SCF data in the literature for many Gaussian-type orbital (GTO) basis sets together with some new values calculated at the (9,5,1) to (13,8,2) levels. Trends in the variation of f within each group of reference molecules from one basis set to another, and the trends in f from one group of reference molecules to another, are discussed in detail. To minimize the influence of these effects in an E_RHF estimate it is recommended that the f value should be derived from reference molecules which possess a similar combination of structural features, i.e., bonded hydrogen, single, double, or triple bonds, and the number of lone-pair electrons. Further calculations show that an f value based on data for closed-shell molecules is not applicable to open-shell species.     

Comparison of basis set superposition error corrected perturbation theories for calculating intermolecular interaction energies

Recently, two different but conceptually similar basis set superposition error (BSSE) free second‐order perturbation theoretical schemes were developed by us that are being based on the chemical Hamiltonian approach (CHA). Using these CHA‐MP2 and CHA‐PT2 methods, a comparison is made between the a posteriori and a priori BSSE correction schemes at the correlated level. Sample calculations are presented for four hydrogen bonded complexes (HFH₃N, HFH₂O, H₂SHF, and H₂OHCl) in nine different basis sets (from 6–31G to TZV**++). The results show that the BSSE content is very significant in the interaction energy if electron correlation is accounted for, so removing the BSSE is very important. The differences of the two perturbational theories discussed are connected solely with the different one electron orbital sets used for building up the unperturbed single determinant wave function. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 274–283, 1999     

Development and testing of a compact basis set for use in effective core potential calculations on rhodium complexes

We present a set of effective core potential (ECP) basis sets for rhodium atoms which are of reasonable size for use in electronic structure calculations. In these ECP basis sets, the Los Alamos ECP is used to simulate the effect of the core electrons while an optimized set of Gaussian functions, which includes polarization and diffuse functions, is used to describe the valence electrons. These basis sets were optimized to reproduce the ionization energy and electron affinity of atomic rhodium. They were also tested by computing the electronic ground state geometry and harmonic frequencies of [Rh(CO)₂μ‐Cl]₂, Rh(CO)₂ClPy, and RhCO (neutral and its positive, and negative ions) as well as the enthalpy of the reaction of [Rh(CO)₂μ‐Cl]₂ with pyridine (Py) to give Rh(CO)₂ClPy, at different levels of theory. Good agreement with experimental values was obtained. Although the number of basis functions used in our ECP basis sets is smaller than those of other ECP basis sets of comparable quality, we show that the newly developed ECP basis sets provide the flexibility and precision required to reproduce a wide range of chemical and physical properties of rhodium compounds. Therefore, we recommend the use of these compact yet accurate ECP basis sets for electronic structure calculations on molecules involving rhodium atoms. © 2012 Wiley Periodicals, Inc.     

Can STO basis sets do a good job in evaluating molecular electromagnetic properties? II: Second hyperpolarizability of H<Subscript>2</Subscript>O,CH<Subscript>4</Subscript> and NH<Subscript>3</Subscript> according to the TDHF theory

The assessment of the performance of STO basis sets for the ab initio estimation of nonlinear electromagnetic response properties of molecules, using a Time Dependent Hartree-Fock procedure, has been extended from the first to the second dynamic hyperpolarizability of three bench polyatomics (H₂O, CH₄, NH₃). Calculations based on extended basis sets are reported and briefly discussed in order to provide a wider perspective on the existing comparisons.     

4‐Styrylquinolines from cyclocondensation reactions between (2‐aminophenyl)chalcones and 1,3‐diketones: crystal structures and regiochemistry

Structures are reported for two matched sets of substituted 4‐styrylquinolines which were prepared by the formation of the heterocyclic ring in cyclocondensation reactions between 1‐(2‐aminophenyl)‐3‐arylprop‐2‐en‐1‐ones with 1,3‐dicarbonyl compounds. (E)‐3‐Acetyl‐4‐[2‐(4‐methoxyphenyl)ethenyl]‐2‐methylquinoline, C₂₁H₁₉NO₂, (I), (E)‐3‐acetyl‐4‐[2‐(4‐bromophenyl)ethenyl]‐2‐methylquinoline, C₂₀H₁₆BrNO, (II), and (E)‐3‐acetyl‐2‐methyl‐4‐{2‐[4‐(trifluoromethyl)phenyl]ethenyl}quinoline, C₂₁H₁₆F₃NO, (III), are isomorphous and in each structure the molecules are linked by a single C—H…O hydrogen bond to form C(6) chains. In (I), but not in (II) or (III), this is augmented by a C—H…π(arene) hydrogen bond to form a chain of rings; hence, (I)–(III) are not strictly isostructural. By contrast with (I)–(III), no two of ethyl (E)‐4‐[2‐(4‐methoxyphenyl)ethenyl]‐2‐methylquinoline‐3‐carboxylate, C₂₂H₂₁NO₃, (IV), ethyl (E)‐4‐[2‐(4‐bromophenyl)ethenyl]‐2‐methylquinoline‐3‐carboxylate, C₂₁H₁₈BrNO₂, (V), and ethyl (E)‐2‐methyl‐4‐{2‐[4‐(trifluoromethyl)phenyl]ethenyl}quinoline‐3‐carboxylate, C₂₂H₁₈F₃NO₂, (VI), are isomorphous. The molecules of (IV) are linked by a single C—H…O hydrogen bond to form C(13) chains, but cyclic centrosymmetric dimers are formed in both (V) and (VI). The dimer in (V) contains a C—H…π(pyridyl) hydrogen bond, while that in (VI) contains two independent C—H…O hydrogen bonds. Comparisons are made with some related structures, and both the regiochemistry and the mechanism of the heterocyclic ring formation are discussed.     

Computational linear dependence in molecular electronic structure calculations using universal basis sets

Distributed universal even‐tempered basis sets have been developed over recent years that are capable of supporting Hartree–Fock energies to an accuracy approaching the sub‐μHartree level. These basis sets have also been exploited in correlation studies, in applications to polyatomic molecules, and in the calculation of electric properties, such as multipole moments, polarizabilities, and hyperpolarizabilities. Jorge and coworkers have also developed universal basis sets and have recently reported applications to diatomic molecular systems. In this article, we compare the molecular calculations reported by Jorge and coworkers with our previous studies. Particular attention is given to the degree of computational linear dependence associated with the various basis sets employed and the consequential effects of the accuracy of the calculated energies. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Multipole expansion of diatomic overlap

The systematic extension of Ruedenberg's expansion formula proposed in Part I [1] is applied to a series of diatomic and polyatomic molecules (BH, NH, HF, Be₂, C₂, F₂, CO, BH₃, CH₄, NH₃, H₂O, HCN and H₂CO). In general, good agreement with the results of full SCF calculations with the same minimum STO basis set is achieved. Thus, the errors due to this integral approximation scheme called MEDO (Multipole Expansion of Diatomic Overlap) are almost negligible compared to those introduced by basis set truncation.     

Preparation,Structure, and Second‐order Nonlinear Optical Properties of a Borate‐Carboxylic Acid Compound: NH4B[d‐(+)‐C4H4O5]2·H2O

The organic‐inorganic hybrid nonlinear optical (NLO) material NH₄B(d‐ (+)‐C₄H₄O₅)₂ · H₂O (NBC) was synthesized in a borate‐carboxylic acid system. Its structure was determined by single crystal X‐ray diffraction. It crystallizes in the orthorhombic system, space group Pna2₁ (No. 33), with cell parameters a = 11.484(6) Å, b = 5.354(3) Å, c = 21.079(12) Å, V = 1296.0(12), Z = 4. It exhibits a three‐dimensional pseudo tunnel structure consisting of fundamental building block [B(d‐ (+)‐C₄H₄O₅)₂]^– anions. The small cavities are occupied by the H₂O molecules and NH₄⁺ cations, which stabilize the whole structure by O–H ··· O and N–H ··· O hydrogen bonds. The powder X‐ray diffraction (PXRD) of the crystal was also recorded. Elemental analyses, FT‐IR and FT‐Raman spectra analyses, thermal analysis, and diffuse‐reflectance spectra for the compound are also presented, as are band structures and density of states calculation. Nonlinear optical measurements indicate that the material has second harmonic generation (SHG) properties and is phase‐matchable.