An augmented effective core potential basis set for the calculation of molecular polarizabilities

Calculations of molecular polarizabilities require basis sets capable of accurately describing the responses of the electrons to an external perturbation. Unfortunately, basis sets that yield suitable quantitative results have traditionally been all-electron sets with large numbers of primitives, making their use computationally intractable even for moderately sized systems. We present a systematic augmentation of the effective core potential basis set of Stevens et al. [J Chem Phys 81, 12 (1984), Can J Chem 70, 612 (1992)] for 39 main group elements based on the procedure used to construct diffuse and polarization functions in the well-known Sadlej basis sets [Collec Czech Chem Comm 53, 1995 (1988)]. Representative calculations have been performed and we have shown that results to within 1% of all-electron calculations using the Sadlej basis set can be obtained for <1-35% of the computational cost using this new basis set.     

A comparative study ofab-initio effective core potential and all-electron calculations for molecular structures and transition states

The reliability of theab-initio effective core potential method for calculating molecular geometries was tested for several polyatomic molecules by using the energy gradient technique. The calculated geometries are in good agreement with those of all-electron calculation not only for equilibrium but also for transition states. The heat of reaction and the activation barrier height compare very well with those of all-electron calculation as well.     

Generalized relativistic effective core potential calculations of the adiabatic potential curve and spectroscopic constants for the ground electronic state of the Ca2 molecule

The potential curve, dissociation energy, equilibrium internuclear distance, and spectroscopic constants for the ground state of the Ca₂ molecule are calculated with the help of the generalized relativistic effective core potential method, which allows one to exclude the inner core electrons from the calculations and to take the relativistic effects into account effectively. Extensive generalized correlation basis sets were constructed and used. The scalar relativistic coupled cluster method with corrections for high‐order cluster amplitudes is used for the correlation treatment. The results are analyzed and compared with the experimental data and corresponding all‐electron results. © 2013 Wiley Periodicals, Inc.     

Atomic orbital basis sets for use with effective core potentials

Basis sets developed for use with effective core potentials describe pseudo‐orbitals rather than orbitals. The primitive Gaussian functions and the contraction coefficients in the basis set must therefore both describe the valence region effectively and allow the pseudo‐orbital to be small in the core region. The latter is particularly difficult using 1s primitive functions, which have their maxima at the nucleus. Several methods of choosing contraction coefficients are tried, and it is found that natural orbitals give the best results. The number and optimization of primitive functions are done following Dunning's correlation‐consistent procedure. Optimization of orbital exponents for larger atoms frequently results in coalescence of adjacent exponents; use of orbitals with higher principal quantum number is one alternative. Actinide atoms or ions provide the most difficult cases in that basis sets must be optimized for valence shells of different radial size simultaneously considering correlation energy and spin‐orbit energy. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 516–520, 2000     

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.     

An approximate frozen core approach to valence only molecular calculations

A simple valence electron-only theory based on an approximate frozen core approach and an exact core-valence strong orthogonality condition is developed for atomic and molecular systems. A unique reduced basis is introduced in which both core and valence orbitals are expanded. The core representation is roughly approximated, and the valence orbital overlap with the corresponding all-electron reference functions is nearly exact. The size of the reduced basis in terms of primitive functions is practically the same as that adopted by effective core potential methods in which the valence orbitals have the correct nodal properties. Results obtained with the present approach are presented for LiO, BeO and CaO molecules, and compared with the corresponding all-electron frozen core calculations. In addition, a detailed investigation on Li _n Be clusters (n=1,..., 6) is carried out.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

A computationally efficient alternative to the Buckingham potential for molecular mechanics calculations

This paper describes a (6-8) variant of the Lennard-Jones (6-12) potential,for computing the energy of non-bonded interactions in molecular mechanicscalculations, which combines the overall precision of the Buckingham (6-exp)potential with the computational efficiency of the standard Lennard-Jones(6-12) potential. There is also a note on the radius of convergence of thefull matrix Newton–Raphson optimization procedure.     

Comparison of the effective core potential and model potential methods in studies of electron correlation energy in molecules: Dihalides and halogen hydrides

Summary The effective core potential and model potential methods were used in post-SCF calculations on HC1, HBr, Cl₂, and Br₂ in order to gain insight into the effect of insufficient representation of inner nodes in the valence orbitals of the approximate methods. The results show that while the correlation energy may be slightly overestimated (by 1–7%), both the electric moment functions and the quantities depending on energy differences are consistently similar for the methods studied and close to the results from all-electron calculations.Dedicated to Prof. Klaus Ruedenberg     

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     

Gaussian basis set of double zeta quality for atoms K through Kr: application in DFT calculations of molecular properties

Contracted basis sets of double zeta (DZ) quality for the atoms from K to Kr are presented. They were determined from fully optimized basis sets of primitive Gaussian-type functions generated in atomic Hartree-Fock calculations. Sets of Gaussian polarization functions optimized at the Möller-Plesset second-order level were added to the DZ basis set. This extends earlier work on segmented contracted DZ basis set for atoms H-Ar. From this set, using the BP86 nonhybrid and B3LYP hybrid functionals, dissociation energy, geometric parameters, harmonic vibrational frequency, and electric dipole moment of a set of molecules were calculated and compared with results obtained with other basis sets and with experimental data reported in the literature. In addition, ⁵⁷Fe and ⁷⁷Se nuclear magnetic resonance chemical shifts in Fe(C₅H₅)₂, H₂Se, and CSe₂ were calculated using density functional theory and gauge-including atomic orbitals and, then, compared with theoretical and experimental values previously published in the literature. Except for chemical shift, one verifies that our results give the best agreement with experimental and benchmark values. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008     

On orthogonality constrained multiple core‐hole states and optimized effective potential method

An attempt to construct a multiple core‐hole state within the optimized effective potential (OEP) methodology is presented. In contrast to the conventional Δ‐self‐consistent field method for hole states, the effects of removing an electron is achieved using some orthogonality constraints imposed on the orbitals so that a Slater determinant describing a hole state is constrained to be orthogonal to that of a neutral system. It is shown that single, double, and multiple core‐hole states can be treated within a unified framework and can be easily implemented for atoms and molecules. For this purpose, a constrained OEP method proposed earlier for excited states (Glushkov and Levy, J. Chem. Phys. 2007, 126, 174106) is further developed to calculate single and double core ionization energies using a local effective potential expressed as a direct mapping of the external potential. The corresponding equations, determining core‐hole orbitals from a one‐particle Schrödinger equation with a local potential as well as correlation corrections derived from the second‐order many‐body perturbation theory are given. One of the advantages of the present direct mapping formulation is that the effective potential, which plays the role of the Kohn–Sham potential, has the symmetry of the external potential. Single and double core ionization potentials computed with the presented scheme were found to be in agreement with data available from experiment and other calculations. We also discuss core‐hole state local potentials for the systems studied. © 2012 Wiley Periodicals, Inc.     

Generalized relativistic effective core potentials for superheavy elements

The generalized relativistic effective core potentials (GRECPs) for calculations of electronic structure and physical-chemical properties of compounds containing superheavy elements (Z ≥ 104) are presented. Features of accounting for the finite nuclear size effects which are unusually large for superheavy elements are discussed in details. Accuracy of the GRECPs is analyzed in atomic calculations compared to all-electron studies with the Dirac-Coulomb-Breit Hamiltonian. Applications of the GRECP method in molecular and cluster calculations are surveyed.     

New out-of-plane angle and bond angle internal coordinates and related potential energy functions for molecular mechanics and dynamics simulations

With currently used definitions of out-of-plane angle and bond angle internal coordinates, Cartesian derivatives have singularities, at ±π/2 in the former case and π in the latter. If either of these occur during molecular mechanics or dynamics simulations, the forces are not well defined. To avoid such difficulties, we provide new out-of-plane and bond angle coordinates and associated potential energy functions that inherently avoid these singularities. The application of these coordinates is illustrated by ab initio calculations on ammonia, water, and carbon dioxide. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1067–1084, 1999     

Prediction of drug solubility from molecular structure using a drug-like training set

Using a training set of 191 drug-like compounds extracted from the AQUASOL database a quantitative structure-property relationship (QSPR) study was conducted employing a set of simple structural and physicochemical properties to predict aqueous solubility. The resultant regression model comprised five parameters (ClogP, molecular weight, indicator variable for aliphatic amine groups, number of rotatable bonds and number of aromatic rings) and demonstrated acceptable statistics (r ² = 0.87, s = 0.51, F = 243.6, n = 191). The model was applied to two test sets consisting of a drug-like set of compounds (r ² = 0.80, s = 0.68, n = 174) and a set of agrochemicals (r ² = 0.88, s = 0.65, n = 200). Using the established general solubility equation (GSE) on the training and drug-like test set gave poorer results than the current study. The agrochemical test set was predicted with equal accuracy using the GSE and the QSPR equation. The results of this study suggest that increasing molecular size, rigidity and lipophilicity decrease solubility whereas increasing conformational flexibility and the presence of a non-conjugated amine group increase the solubility of drug-like compounds. Indeed, the proposed structural parameters make physical sense and provide simple guidelines for modifying solubility during lead optimisation.     

Implementation of atomic basis set composed of 1s Gaussian and 1s Slater-type orbitals to carry out quantum mechanics molecular calculations

A mixed atomic basis set formed with ls Slater-type orbitals and 1s floating spherical Gaussian orbitals is implemented. Evaluation of multicenter integrals is carried out using a method based on expansion of binary products of atomic basis functions in terms of a complete basis set, and a systematic analysis is performed. The proposed algorithm is very stable and furnishes fairly good results for total energy and geometry. An LCAO-SCF test calculation is carried out on LiH. The trends observed show that there are some combinations of mixed orbitals that are appropriate to describe the system. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 604–609, 1999     

New program for molecular calculations with Slater‐type orbitals

A new program for computing all the integrals appearing in molecular calculations with Slater‐type orbitals (STO) is reported. This program follows the same philosophy as the reference pogram previously reported but introduces two main changes: Local symmetry is profited to compute all the two‐electron integrals from a minimal set of seed integrals, and a new algorithm recently developed is used for computing the seed integrals. The new code reduces between one and two orders of magnitude the computational cost in most polyatomic systems. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 148–153, 2001     

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).