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 systematic preparation of new contracted Gaussian-type orbital sets. III. Second-row atoms from Li through ne

Four minimal Gaussian basis sets are generated for the second-row atoms Li through Ne. The first one, MINI-1, consists of a 3-term contraction of primitive Gaussian-type orbitals for 1s, 2s, and 2p atomic orbitals. The convenient shorthand notation would be (3,3) for Li? Be and (3,3/3) for B? Ne. The second one, MINI-2, can be represented by (3,3/4) for B? Ne. In the same way, MINI-3 is described as (4,3) for Li? Be, and MINI-3 and MINI-4 are represented by (4,3/3) and (4,3/4) for B? Ne, respectively. Although the four basis sets are the minimal type, they give the valence shell orbital energies which are close to those of DZ. These four and other sets derived from them are tested for the hetero- and homodiatomic molecules and some organic molecules. They are found to give the orbital energies that agree well with those given by extended calculations. Atomization energies and other spectroscopic constants are also calculated and compared with those of extended calculations. The results clearly indicate that the present basis sets can be used very effectively in the molecular calculations.     

Compact contracted Gaussian-type basis sets for halogen atoms. Basis-set superposition effects on molecular properties

Compact, contracted Gaussian basis sets for halogen atoms are generated and tested in ab initio molecular calculations. These basis sets have similar structure to that of Huzinaga and co-workers' (HTS ) sets; however, they give both better atomic total energies and better properties of atomic valence orbitals. These sets, after splitting of valence orbitals and augmenting with polarization functions, provide molecular results that agree well with those given by extended calculations. Basis set superposition error (BSSE ) is calculated using the counterpoise method. BSSE has only slight influence on calculated equilibrium geometry, shape of potential curve, and electric properties (dipole and quadrupole moments) of molecules. However, atomization energies may be significantly changed by the BSSE .     

The influence of basis sets on wave function tails

Wave function tails are analyzed quantitatively by investigating the dependence of exterior electron density (EED ) on basis sets; the EED is defined as the integrated electron density outside the repulsive molecular surface. Ab initio MO calculations with large scale basis sets were performed to establish the benchmark order of EED values for valence orbitals of some simple molecules. It is found that very popular basis sets, such as 4-31G, which are determined by energy optimization, are inferior in describing the wave function tails to some similar size basis sets, such as MIDI -4, which are obtained by least-squares fit to near Hartree-Fock atomic functions. Further the EED values for atomic 2s functions are shown to be unfavorably smaller than those for atomic 2p functions when the same value is used for the exponent α in the GTO basis sets. This indicates that the frequently used constraint α_s = α_p is not appropriate for describing wave function tails with medium-size basis sets. Deficiencies in the energy-optimized basis sets are found to become more serious for molecules including heavier atoms.     

Study of locally dense and locally saturated basis sets in localized molecular orbital calculations of nuclear shielding: Ab initio LORG calculations for 13C and 17O in norbornenone

This study demonstrates the use of uneven atomic basis sets for ab initio calculations of NMR shielding in the localized orbital/local origin (LORG) approach with norbornenone as the test case. We distinguish between locally dense sets (extended basis on target atom only) and locally saturated sets (extended bases on target atom and atoms in its first bonding sphere), using 6-311G ** and 6-31G sets to describe the high and low level of function sets. It is shown that the use of these uneven sets can simulate high basis set level calculations of shieldings for ¹H and for all the ¹³C nuclei in this molecule and, hence, allows quite accurate ab initio calculations of shielding properties of these nuclei in large molecules using relatively modest computational facilities. The shielding of the double-bonded ¹⁷O nucleus is apparently sensitive to basis-set quality beyond the first bonding sphere. © 1996 John Wiley & Sons, Inc.     

Supplementary d and f functions in molecular wave functions at large and small internuclear separations

The CO, CO₂, CS, CIF, and SO₂ molecules were used to test the dependence of supplementary d and f function exponents to changes in bond lengths and bond angles in MO calculations utilizing Gaussian basis sets in Hartree–Fock and Moller–Plesset calculations. Using Dunning–Hay double zeta basis sets, optimizations were performed at internuclear separations from 100–200 pm and beyond. The energy cost of not reoptimizing d function exponents when bonds are stretched or compressed is much smaller for correlated calculations than for those at the Hartree–Fock level and is greatest at the lower end of the range of internuclear distances. The problem is much less serious at all levels when multiple sets of d functions are used. © 1993 John Wiley & Sons, Inc.     

Construction of basis sets of hybrid atomic orbitals for describing the nonequivalent bonds of an atom with three neighboring atoms (sp 2 andsp 3 hybridization)

The paper describes methods for obtaining basis sets of sp² and sp³ hybrid atomic orbitals to describe nonequivalent chemical bonds in organic molecules with heteroatoms. Being affine, these basis sets present an alternative to the conventional basis sets of Cartesian atomic orbitals. Unlike the latter, the hybrid atomic orbitals are invariant to spatial rotations of molecules, thus providing the rotational invariance of the results of any semiempirical quantum chemical calculations. The construction of the basis sets of hybrid functions for atoms surrounded with three neighboring atoms (planar and nonplanar configurations) is considered in detail. V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 36. No. 6, pp. 963–968, November–December, 1995. Translated by I. Izvekova     

Cubic-grid Gaussian basis sets for electron scattering calculations. I. Definition and construction

We propose a new type of Gaussian basis sets for use in calculations of electron scattering by molecules. Instead of locating the basis-set functions on the atomic centers of the target molecule, we place primitive s-type Gaussians at the positions of a cubic lattice with a regular grid. The grid and the Gaussian exponent are fixed so as to give the best representation of the plane-wave function. Plane-wave functions and Green functions obtained by means of the cubic-grid basis set are tested graphically against exact functions and functions expressed by means of a conventional Gaussian basis set. © 1995 John Wiley & Sons, Inc.     

Ab initio and molecular mechanics study of n-phenyl phthalimide and its crystal structure

Ab initio molecular orbital calculations are reported on the energetics for torsional motion of N-phenyl phthalimide using 3-21G, 6-31G, and 6-31G^** basis sets and incorporating electron correlation effects for selected geometries. With the largest basis set, a minimum energy is found for a torsion angle of 59.2°. Atomic charges are assigned to the molecules on the basis of a least-squares fit to the molecular electrostatic potential. This information is then used in molecular mechanics calculations of the crystal structure, where the calculated unit cell parameters are in good agreement with those observed experimentally.     

Segmented contracted basis sets for atoms H through Xe: Sapporo-(DK)-<Emphasis Type="Italic">n</Emphasis>ZP sets (<Emphasis Type="Italic">n</Emphasis> = D,T, Q)

For the 54 atoms from H to Xe, compact yet accurate segmented Gaussian-type basis sets have been constructed for all electron calculations. Non-relativistic nZP (Sapporo-nZP) sets for Li–Xe and relativistic nZP (Sapporo-DK-nZP) sets for K–Xe are developed (n = D, T, Q), which efficiently incorporate valence and core electron correlations. Test calculations at the coupled-cluster level of theory are performed for spectroscopic constants of 12 hydrides of s- and d-block atoms and 12 diatomics of p-block atoms in their ground states. For all molecules, the calculated spectroscopic constants approach to the experimental values smoothly as the basis set quality increases.     

Contracted Gaussian-type basis functions revisited. III. Atoms K through Kr

Six minimal basis sets of contracted Gaussian-type functions (GTFs) are developed for the third-row atoms K through Kr. The smallest and largest sets for transition metal atoms are (3333/33/3) and (8433/84/8), respectively, where a slash distinguishes the s, p, and d symmetries and single-digit figures in the parentheses denote the numbers of primitive GTFs. The two largest sets, (7433/74/7) and (8433/84/8), surpass the (62111111/33111/311) set of Schaefer et al. in the associated total energies. Our (8433/84/8) set is also superior to their (842111/631/411) set. The quality of the present basis sets is tested by self-consistent field (SCF) and configuration interaction (CI) calculations on the Cu₂ molecule. As the accuracy of the basis set increases, SCF calculations show a decrease in the dissociation energy and an increase in the equilibrium internuclear distance. The same tendencies are found in the results of CI calculations with and without a Davidson correction. All the present basis sets are freely available at the internet address: http://202.35.198.41/∼htatewak/. Received: 17 June 1998 / Accepted: 4 August 1998 / Published online: 23 November 1998     

Quasirelativistic energy-consistent 5f-in-core pseudopotentials for trivalent actinide elements

Quasirelativistic energy-consistent 5f-in-core pseudopotentials modelling trivalent actinides, corresponding to a near-integral 5f ⁿ occupation (n = 0–14 for Ac–Lr), have been generated. Energy-optimized (6s5p4d), (7s6p5d), and (8s7p6d) primitive valence basis sets contracted to polarized double to quadruple zeta quality as well as 2f1g correlation functions have been derived. Corresponding smaller basis sets (4s4p3d), (5s5p4d), and (6s6p5d) suitable for calculations on actinide(III) ions in crystalline solids form subsets of these basis sets designed for calculations on neutral molecules. Results of Hartree–Fock test calculations for actinide(III) monohydrates and actinide trifluorides show a satisfactory agreement with corresponding calculations using 5f-in-valence pseudopotentials. Even in the beginning of the actinide series, where the 5f shell is relatively diffuse, only quite acceptable small deviations occur as long as the 5f-shell does not participate significantly in covalent bonding. Electronic Supplementary Material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Quasirelativistic energy-consistent 5f-in-core pseudopotentials for divalent and tetravalent actinide elements

Quasirelativistic energy-consistent 5f-in-core pseudopotentials modeling divalent (5f ⁿ⁺¹ occupation with n = 5–13 for Pu–No) respectively tetravalent (5f ^n-1 occupation with n = 1–9 for Th–Cf) actinides together with corresponding core-polarization potentials have been generated. Energy-optimized (6s5p4d) and (7s6p5d) valence basis sets as well as 2f1g correlation functions have been derived and contracted to polarized double, triple, and quadruple zeta quality. Corresponding smaller (4s4p) and (5s5p) respectively (4s4p3d) and (5s5p4d) basis sets suitable for calculations on actinide(II) respectively actinide(IV) ions in crystalline solids form subsets of these basis sets designed for calculations on molecules. Results of Hartree–Fock test calculations for actinide di- and tetrafluorides show a satisfactory agreement with calculations using 5f-in-valence pseudopotentials. Electronic Supplementary Material The online version of this article doi: contains supplementary material, which is available to authorized users.     

Ab initio crystal structure predictions for flexible hydrogen‐bonded molecules. Part II. Accurate energy minimization

A method is described to perform ab initio energy minimization for crystals of flexible molecules. The intramolecular energies and forces are obtained directly from ab initio calculations, whereas the intermolecular contributions follow from a potential that had been parameterized earlier on highly accurate quantum‐chemical calculations. Glycol and glycerol were studied exhaustively as prototypes. Lists of hypothetical crystal structures were generated using an empirical force field, after which ab initio energy minimizations were performed for a few hundreds of these. The experimental crystal structures were found among the structures with lowest energy, provided that sufficiently large basis sets were used. Moreover, their crystal geometries were well reproduced. This approach enables a systematic comparison between the merits of force fields at various levels of sophistication. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 805–815, 2001     

A note on the importance of d orbitals in the calculation of effective interactions and the excitation spectra of atoms and molecules

The focal point of our discussion is the examination of truncated basis sets used in obtaining an accurate first principles clculation of the effective valence shell Hamiltonian by the canonical transformation-cluster expansion approasch. Subsequent diagonalization of this effecitve valence shell hamiltonian yields the valence shell transition energies. A detailed analysis of numerical results obtained using a number of different basis sets of hydrogen-like orbitals together with rigorous symmetry arguments celarly demonstrates the special role played by d orbitals in computing the ³P → ¹D transition energy in carbon. The failure of early attempts to calculate the effective Hamiltonian for ethylene from first principles is examined in the light of recent ab initio calculations on ethylene involving d orbitals and the computations reported in this paper. We conclude that accurate calculations of the effective valence shell Hamiltonian for molecules must consider d orbitals in the excited orbital basis set.     

Substituent effects in second-row molecules: Basis set performance in calculations of normal valency phosphorus and sulfur compounds

Ab inito molecular orbital calculations of the phosphorus- and sulfur-containing series PH₂X, PH₃X⁺, SHX, and SH₂X⁺ (X = H, CH₃, NH₂, OH, F) have been carried out over a range of Gaussian basis sets and the results (optimized geometrical structures, relative energies, and electron distributions) critically compared. As in first-row molecules there are large discrepancies between substituent interaction energies at different basis set levels, particularly in electron-rich molecules; use of basis sets lower than the supplemented 6-31G basis incurs the risk of obtaining substituent stabilizations with large errors, including the wrong sign. Only a small part of the discrepancies is accounted for by structural differences between the optimized geometries. Supplementation of low level basis sets by d functions frequently leads to exaggerated stabilization energies for π-donor substituents. Poor performance also results from the use of split valence basis sets in which the valence shell electron density is too heavily concentrated in diffuse component of the valence shell functions, again likely to occur in electron-rich molecules. Isodesmic reaction energies are much less sensitive to basis set variation, but d function supplementation is necessary to achieve reliable results, suggesting a marginal valence role for d functions, not merely polarization of the bonding density. Optimized molecular geometries are relatively insensitive to basis set and electron population analysis data, for better-than-minimal bases, are uniform to an unexpected degree.     

Some theoretical aspects of vibrational fine structure accompanying core ionizations in N2 and CO

Ab initio calculations have been carried out on CO and N₂ and the relevant core hole states with different basis sets to investigate differences in geometries and force constants. From these calculations vibrational band profiles of the core level ESCA spectra for these molecules have been interpreted, obviating the need to rely on data pertaining to the equivalent core species. The agreement with experimental profiles is excellent. The O_1s level of CO which has not been subjected to detailed theoretical analysis previously, is predicted to show substantial vibrational structure in excellent agreement with recently acquired experimental data. The effect of temperature on the band profiles has also been considered. Theoretically derived core binding and relaxation energies of these systems have been investigated both as a function of basis set, and of internuclear distance. Density difference contours have been computed and give a straightforward pictorial representation of the substantial electron reorganizations accompanying core ionizations. Small basis sets with valence exponents appropriate to the equivalent core species when used in hole state calculations describe bond lengths, force constants, core binding energies and relaxation energies with an accuracy comparable to that appropriate to the corresponding extended basis set calculations.     

Polarized basis sets for accurate calculations of static and dynamic electric properties of molecules

We report on the development and testing of large polarized basis sets (LPolX, where X is the element symbol) for accurate calculations of linear and nonlinear electric properties of molecules. The method used to generate LPolX sets is based on our studies of the analytic dependence of Gaussian functions on external time‐independent and time‐dependent electric fields. At variance with the earlier investigations of small, highly compact (ZPolX) basis sets for moderately accurate calculations of electric properties of large molecules, the present goal is to obtain basis sets that are nearly saturated with respect to the selected class of electric properties and can be used for accurate studies of interaction‐induced properties. This saturation makes the LPolX sets also useful in calculations of optical properties for chiral molecules. In this article, the LPolX sets are generated for X = H, C, N, O, and F, and examined in calculations of linear and nonlinear electric properties of four standard test systems: HF, N₂, CO, and HCN. The study of the performance of LPolX basis sets has been carried out at different levels of approximation ranging from the SCF HF method to highly correlated CCSD(T) approach. The results obtained in this study compare favorably with accurate reference data and show a high level of saturation of LPolX basis sets with respect to the polarization effect due to external electric fields. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Removal of dependencies from nearly complete basis sets. Calculations on the helium dimer

A method is devised for dealing with almost linearly dependent basis sets that contain large sets of bond functions. Using the largest of such basis sets, LARSAT, the second-order Møller-Plesset polarization dispersion energy of the helium dimer is calculated to be - 17.08 K at R = 5.6 bohrs. MR-SDCI calculations, employing a set of 37 reference configurations, were performed for the helium dimer with several basis sets at 4.0 and 5.6 bohrs. Size-extensivity corrections were included to take into account the R dependency of the size-extensivity error in MR-SDCI calculations. The He₂ interaction energies computed with basis LARSAT are - 10.92 K at 5.6 bohrs and 295.1 K at 4.0 bohrs. The 37-MR-SDCI calculations with basis LARSAT almost reproduce the He₂ full configuration interaction (CI) interaction energies computed with the same basis, at notably smaller cost. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 805–815, 1997     

Ab initio studies on several species of the formula X3YO and X3YOH

Ab initio molecular orbital calculations using both minimal and extended basis sets have been applied to two isoelectronic sets of molecules. One set corresponds to the 18 electron species H₃NO, H₃CO^– and H₃COH while the second set contains the 42 electron fluorinated molecules F₃NO, F₃CO^– and F₃COH. The geometries of these molecules have been optimized, using both the minimal STO-3G and the extended 4-31G basis sets. These comparative calculations reveal that the 4-31G basis produced structural parameters in much better agreement with experiment. The effect of includingd-orbitals in the basis set was also investigated. For the fluorinated oxides it has been found that the optimized 4-31G structures were only slightly altered by the addition ofd-orbitals. For H₃NO, on the other hand, the inclusion ofd-orbitals considerably shortens the N-O bond distance. Both H₃NO and CF₃OH, which are unknown experimentally, are theoretically predicted to be capable of existence. The electronic structures of these molecules have also been examined using electronic partitioning according to the Mulliken scheme.