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.     

Computational convergence of electronic structure calculations of transition metal ligand complexes

Calculations of binding energies and optimum geometries of compounds of the series M(H₂O)⁺ with M = Sc to Zn have been carried out and compared with gas-phase experimental data and with the Rosi and Bauschlicher MCPF calculations. Hartree–Fock calculations and correlated calculations at MP2, MP4, and QCISD(T) levels were used to test the dependence of the results upon the level of correlation. A test of basis set dependence was also carried out, using parallel calculations on four basis sets ranging in size from a small DZ set to a TZ contraction. Correlation levels above MP2 and elaboration of the metal d-function basis set to (4d/3d) size or greater were both necessary for convergence with the most uniformly reliable results obtained from QCISD(T) calculations on a basis set with a (6d/4d) contraction for the d-function space. However, MP2 or higher-level calculations with a contracted four or five d function set [(5d/3d) or (4d/3d)] are capable of yielding results on binding energies and geometries close to the current gas-phase experimental uncertainty on electrostatically bound transition metal complexes. © 1993 John Wiley & Sons, Inc.     

Core ionization potentials from self-interaction corrected Kohn-Sham orbital energies

We propose a simple self-interaction correction to Kohn-Sham orbital energies in order to apply ground state Kohn-Sham density functional theory to accurate predictions of core electron binding energies and chemical shifts. The proposition is explored through a series of calculations of organic compounds of different sizes and types. Comparison is made versus experiment and the "DeltaKohn-Sham" method employing separate state optimizations of the ground and core hole states, with the use of the B3LYP functional and different basis sets. A parameter alpha is introduced for a best fitting of computed and experimental ionization potentials. It is found that internal parametrizations in terms of basis set expansions can be well controlled. With a unique alpha=0.72 and basis set larger than 6-31G, the core ionization energies (IPs) of the self-interaction corrected Kohn-Sham calculations fit quite well to the experimental values. Hence, self-interaction corrected Kohn-Sham calculations seem to provide a promising tool for core IPs that combines accuracy and efficiency.     

Minimal basis study of inner-shell ionization potentials for molecules containing sulfur: S,S-Diphenyl-N-p-Tolylsulfonyl-Sulfilimine

Ab initio calculations with a minimal (STO -3G) basis set on a number of sulfur-containing molecules are used to show that Koopmans' theorem and minimal basis calculations may be a simple but adequate way of obtaining inner-shell ionization potentials and chemical shifts of large molecules. The x-ray photoelectron spectrum of (C₆H₅)₂SNSO₂C₆H₄CH₃ is discussed with reference to an ab initio SCF minimal basis calculation on the model molecule H₂SNSO₂H.     

Basis sets for geometry optimizations of second-row transition metal inorganic and organometallic complexes

Modest-sized basis sets for the second-row transition metal atoms are developed for use in geometry optimization calculations. Our method is patterned after previous work on basis sets for first-row transition metal atoms. The basis sets are constructed from the minimal basis sets of Huzinaga and are augmented with a set of diffuse p and d functions. The exponents of these diffuse functions are chosen to minimize both the difference between the calculated and experimental equilibrium geometries and the total molecular energies for several second-row transition metal inorganic and organon etallic complexes. Slightly smaller basis sets, based on the same Huzinaga minimal sets but augmented with a set of diffuse s and p functions rather than diffuse p and d functions, are also presented. The performance of these basis sets is tested on a wide variety of second-row transition metal inorganic and organometallic complexes and is compared to pseudopotential basis sets incorporating effective core potentials.     

Accurate ab initio binding energies of alkaline earth metal clusters

The effects of basis set superposition error (BSSE) and core-correlation on the electronic binding energies of alkaline earth metal clusters Y(n) (Y = Be, Mg, Ca; n = 2-4) at the Moller-Plesset second-order perturbation theory (MP2) and the single and double coupled cluster method with perturbative triples correction (CCSD(T)) levels are examined using the correlation consistent basis sets cc-pVXZ and cc-pCVXZ (X = D, T, Q, 5). It is found that, while BSSE has a negligible effect for valence-electron-only-correlated calculations for most basis sets, its magnitude becomes more pronounced for all-electron-correlated calculations, including core electrons. By utilizing the negligible effect of BSSE on the binding energies for valence-electron-only-correlated calculations, in combination with the negligible core-correlation effect at the CCSD(T) level, accurate binding energies of these clusters up to pentamers (octamers in the case of the Be clusters) are estimated via the basis set extrapolation of ab initio CCSD(T) correlation energies of the monomer and cluster with only the cc-pVDZ and cc-pVTZ sets, using the basis set and correlation-dependent extrapolation formula recently devised. A comparison between the CCSD(T) and density functional theory (DFT) binding energies is made to identify the most appropriate DFT method for the study of these clusters.     

Ab initio calculations of guanidinium–carboxylate interaction

Ab initio calculations (self-consistent-field Hartree–Fock) using 6-31G and STO -4G basis sets are used to investigate the interaction between guanidinium and methylguanidinium ion with the carboxylate group of formate. Binding energies and optimum geometries are obtained and compared with reported results using a smaller basis set (STO -3G). The importance of this interaction in proteinsubstrate binding is discussed.     

Additivity model for calculations of UHF spin densities in some aza-aromatic radical anions

The concept of a universal basis set for electronic structure calculation is illustrated by presenting results obtained when basis sets are transferred from one atom to another. A single Slater-orbital basis set, consisting of nine 1s and six 2p functions, produces Hartree-Fock total energies and orbital energies in good agreement with the most accurate calculations of these energies obtained using different basis sets individually optimized for each atom. Transferability of integrals is a natural consequence of the use of the same basis set for each atom in a molecule.     

Study on the behavior of energy convergence in ab initio crystal orbital calculations

Summary This article studies the dependence on the cutoff scheme of ab initio crystal orbital calculations with no long-range correction. We have thoroughly studied the Namur cutoff and cell-wise cutoff schemes through calculations of polyethylene and LiH chains. The Namur cutoff gives the fastest energy convergence with respect to the number of neighbors (N ₀). The energy convergence behavior with respect to N ₀ depends on the basis set. The Namur cutoff shows the fastest convergence with the STO-3G basis set, intermediate convergence with the MINI basis set, and the slowest convergence with the (7s4p/3s) basis set. The cell-wise cutoff shows exactly the reverse order of the Namur cutoff. The Namur cutoff destroys the translational symmetry. Both the Namur cutoff and cell-wise cutoff schemes introduce slight asymmetry on the two equivalent C-C bonds of polyethylene when calculating with a C₂H₄ unit cell. The asymmetry with the Namur cutoff can be made to disappear by increasing N ₀ a little. The calculations on two different unit-cell structures of trans-polyacetylene show the effect of the cutoff scheme on the total energy. Only the symmetric cutoff energies are the same. Disagreement related to the Namur cutoff disappears at N ₀ = 20, however, that related to the cell-wise and modified symmetric cutoff schemes remains at N ₀ 20. The optimized geometry and vibrational frequency are not as sensitive to the cutoff method except with the symmetric cutoff. A compilation of all results shows that the Namur cutoff is the superior cutoff scheme when calculating the insulator using the minimal basis set, especially the STO-3G basis set.     

Optimization of virtual orbitals in the framework of a multiconfiguration spin-coupled wave function

A new method is introduced for the optimization of nonorthogonal virtual orbitals for use in general multiconfiguration spin-coupled wave functions. The use of a number of highly effective approximations greatly reduces the computational effort involved, the most important being the use of a second-order perturbation expression for the energy and an approximate expression for the elements of the Hessian. As a result, the overall scheme scales very favourably with respect to the numbers of active electrons and of basis functions, making it suitable for the accurate study of large systems. Benchmark calculations are presented for the dissociation of LiH(X¹Σ⁺) and Li₂(X¹Σ⁺ _g ) using a highly compact four-configuration wave function. Standard spin-coupled valence bond expansions in the same virtual space are required to be significantly larger before equivalent results are obtained. The results are shown to compare very favourably with full valence complete active space self-consistent field calculations using an identical basis, and binding energies are within 4% of the values obtained from full configuration interaction calculations in the same basis set. Received: 10 June 1997 / Accepted: 7 October 1997     

A theoretical investigation of electronic reorganizations accompanying core and valence ionization in simple hydrogen bonded systems

Non-empirical LCAO MO SCF calculations have been carried out on the ground state and core ionized states of some hydrogen bonded dimers, and in the particular case of H₂O the trimer has also been investigated. Comparison of absolute and relative binding energies and relaxation energies with respect to the corresponding monomers reveals that substantial changes occur in going to the associated species. The relaxation energies for a given core hole are shown to increase on going from monomer to dimer indicating that intermolecular contributions to relaxation energies are of the same sign irrespective of the sign for the shift in core binding energy. Creation of a core hole in the dimer species is shown to give rise to substantial changes in hydrogen bond energies compared with the neutral species. In the particular case of valence holes dominantly of 2s and 2p character it is shown that trends in shifts and relaxation energies parallel those for the core hole states.     

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     

Study of the formamide–methanol dimer with ab initio and density functional theory methods

For the first time, the structures and energies for the hydrogen bonding of a 1:1 complex formed between formamide and methanol molecules have been computed with various pure and hybrid density functional theory (DFT) and ab initio methods at varied basis set levels from 6‐31g to 6‐31+g(d,p). Five reasonable geometries on the potential energy surface of methanol and formamide system are considered and their relative stability is discussed. The infrared (IR) spectrum frequencies, IR intensities, and vibrational frequency shifts are reported. From the systematic studies, it is found that all the DFT methods selected here correctly compute the dimerization energies and geometries, with the B3P86 method predicting the hydrogen bond lengths relatively shorter and BPW91 yielding the interaction energies relatively lower. Finally, the solvent effects on the geometries of the formamide–methanol complexes have also been investigated using self‐consistent reaction field (SCRF) calculations with five different DFT methods at the 6‐31+g(d,p) basis set level. The results indicate that the polarity of the solvent has played an important role on the structures and relative stabilities of different isomers. Moreover, the basis set superposition error correction is critical to the interaction energies in the polar solvents. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Accurate ab intio determination of binding energies for rare-gas dimers by basis set extrapolation

To investigate the electron correlation effect on the binding energies of very weakly bound complexes at highly correlated levels, an extrapolation scheme exploiting the convergent behavior of the binding energy differences between two correlation levels with the correlation-consistent basis set aug-cc-pVXZ was explored. The scheme is based on extrapolating the binding energy differences between the lower and higher correlation levels (such as second-order Møller–Plesset perturbation theory and the single and double coupled-cluster method with perturbative triple correction level), CCSD(T), by X^–3 for relatively small basis set calculations to estimate the corresponding basis set limit, which is then added to the complete basis set(CBS) limit binding energy at the lower correlation level to derive the CBS limit binding energy at the higher level. Test results on rare-gas dimers Rg₂ (Rg is He, Ne, Ar) show that the CCSD(T) CBS limit binding energies estimated by this scheme with aug-cc-pVXZ and aug-cc-pV(X+1)Z basis sets are more accurate than the CBS limit estimated by direct extrapolation of correlation energies by X^–3 with aug-cc-pV(X+1)Z and aug-cc-pV(X+2)Z basis sets in most cases, which signifies the utility of the proposed extrapolation scheme as the level of electron correlation treatment increases. The nonnegligible discrepancy in the well depth near equilibrium between the experimental and the full connected single, double, and triple coupled-cluster method CBS limit estimate obtained by this procedure in the case of Ar₂ suggests that the previous semiempirical potential may be too attractive near equilibrium compared with the actual one.Acknowledgement The major portion of this work was carried out while the author was visiting the Quantum Theory Project (QTP) at the University of Florida. The author is thankful to Rodney Bartlett for hospitality and support during the visit. The author is also thankful to Ajith Perera for assistance in using the ACESII program package. Computational support from the QTP at the University of Florida and the Institute for Basic Science at Ajou University is gratefully acknowledged.     

Application of combined Hartree–Fock–Roothaan theory to molecules with arbitrary number of closed and open shells

In this study, the applicability of the combined Hartree–Fock–Roothaan (CHFR) theory of atomic-molecular and nuclear systems (Guseinov, J Math Chem 42:177, 2007) to the molecules is demonstrated using minimal basis set of Slater type orbitals (STO). As an example of application of CHFR theory, the calculations have been performed for the ground state of electronic configuration of methylene molecule CH ₂ which has two open shells. The results of computer calculations for the orbital, kinetic and total energies, linear combination coefficients of symmetrized molecular orbitals and virial ratios are presented.     

“Spectroscopic” Calculations of CH Bond Dissociation Energies for Ethane, Propane, Butane, Isobutane, Pentane, Hexane, and Neopentane Using Fundamental Vibration Frequencies

The fundamental spectrum and the parameters of the potential function of a number of saturated hydrocarbon molecules are calculated in an anharmonic approximation. The calculation is performed by the variational technique using a minimal Morse-harmonic basis. The potential function is taken as the sum of the Morse function for CH bonds and the harmonic function for the skeletal and deformation vibrations. The initial approximation for the potential function is found by ab initio calculations in a 6-31G basis and refined by solving the inverse problem. The calculated CH bond dissociation energies depend significantly on the molecular structure and on the position of CH bonds in the molecule. These energies correlate well with the experimental cleavage energies of these bonds. The changes in the dipole moment of the molecule induced by vibrations were found by ab initio calculations in a 6-31G basis. The calculated IR transmission curves are in good agreement with the experimental curves.     

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.     

Accurate lattice energies of organic molecular crystals from periodic turbomole calculations

Accurate lattice energies of organic crystals are important i.e. for the pharmaceutical industry. Periodic DFT calculations with atom‐centered Gaussian basis functions with the Turbomole program are used to calculate lattice energies for several non‐covalently bound organic molecular crystals. The accuracy and convergence of results with basis set size and k‐space sampling from periodic calculations is evaluated for the two reference molecules benzoic acid and naphthalene. For the X23 benchmark set of small molecular crystals accurate lattice energies are obtained using the PBE‐D3 functional. In particular for hydrogen‐bonded systems, a sufficiently large basis set is required. The calculated lattice energy differences between enantiopure and racemic crystal forms for a prototype set of chiral molecules are in good agreement with experimental results and allow the rationalization and computer‐aided design of chiral separation processes. © 2018 Wiley Periodicals, Inc.