Correlation balance in basis sets for electronic structure calculations

The balanced addition of polarization functions to the 6–31G and 6–311G basis sets for correlated wave functions is evaluated using bond energy predictions at the MP 2 and full MP 4 levels as a measure of correlation-balanced basis sets. The homolytic dissociations of the XH bonds in H₂, CH₄, NH₃, H₂O, and HF and the XY bonds in C₂H₆, NH₂NH₂, HOOH, and CH₃OH are used as the basis for the evaluation. It is found that correlation balance is achieved for HH, XH, and XY bonds, particularly at the MP 2 level, only if at least as many polarization sets, and sometimes more, are added to the hydrogens as are added to the heavy atoms.     

Extrapolating to the one-electron basis-set limit in electronic structure calculations

A simple, yet reliable, scheme based on treating uniformly singlet-pair and triplet-pair interactions is suggested to extrapolate atomic and molecular electron correlation energies calculated at two basis-set levels of ab initio theory to the infinite one-electron basis-set limit. The novel dual-level method is first tested on extrapolating the full correlation in single-reference coupled-cluster singles and doubles energies for the closed-shell systems CH2((1)A1), H2O, HF, N2, CO, Ne, and F2 with correlation-consistent basis sets of the type cc-pVXZ (X=D,T,Q,5,6) reported by Klopper [Mol. Phys. 6, 481 (2001)] against his own benchmark calculations with large uncontracted basis sets obtained from explicit correlated singles and doubles coupled-cluster theory. Comparisons are also reported for the same data set but using both single-reference Moller-Plesset and coupled-cluster doubles methods. The results show a similar, often better, accordance with the target results than Klopper's extrapolations where singlet-pair and triplet-pair energies are extrapolated separately using the popular X(-3) and X(-5) dual-level laws, respectively. Applications to the extrapolation of the dynamical correlation in multireference configuration interaction calculations carried out anew for He, H2, HeH+, He2 ++, H3+(1 (1)A'), H3+(1 (3)A'), BH, CH, NH, OH, FH, B2, C2, N2, O2, F2, BO, CO, NO, BN, CN, SH, H2O, and NH3 with standard augmented correlation-consistent basis sets of the type aug-cc-pVXZ (X=D,T,Q,5,6) are also reported. Despite lacking accurate theoretical or experimental data for comparison in the case of most diatomic systems, the new method also shows in this case a good performance when judged from the results obtained with the traditional schemes which extrapolate using the two largest affordable basis sets. For the Hartree-Fock and complete-active space self-consistent field energies, a simple pragmatic extrapolation rule is examined whose results are shown to compare well with the ones obtained from the best reported schemes.     

Distributed basis sets of s-type Gaussian functions for molecular electronic structure calculations: Applications of the Gaussian cell model to one-electron polycentric linear molecular systems

A particular formulation of the distributed Gaussian basis-set approach, the extended Gaussian cell model, is applied to the simplest polycentric molecule, the linear H₃²⁺ ion. Calculations of the total energy using two extensions of the original Gaussian cell model are described and results are reported for the ground state and the first excited state. A comparison with recently reported finite element calculations is made for a number of nuclear geometries. © 1996 John Wiley & Sons, Inc.     

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     

Molecular conformations and relative stabilities can be as demanding of the electronic structure method as intermolecular calculations

We have performed a variety of high-level electronic structure calculations on two moderately sized organic molecules and found considerable sensitivity of the intramolecular potential energy surface to the method employed. The gas-phase structure of tyrosine-glycine varies qualitatively between B3LYP and MP2 optimizations, producing different close contacts between the tyrosine ring and the glycine moiety. The relative energies of the 2-(acetylamino)benzamide conformations found in its two polymorphs can vary by over 20 kJ mol-1 between MP2 and B3LYP calculations, using the same basis set. It is shown by a novel analysis that the intramolecular equivalent of basis set superposition error competes with the errors in the intramolecular dispersion in causing this sensitivity.     

The Cassie equation: how it is meant to be used

A review of literature shows that the majority of papers cite a potentially incorrect form of the Cassie and Cassie-Baxter equations to interpret or predict contact angle data. We show that for surfaces wet with a composite interface, the commonly used form of the Cassie-Baxter equation, cosθ(c)=f(1)cosθ-(1-f), is only correct for the case of flat topped pillar geometry without any penetration of the liquid. In general, the original form of the Cassie-Baxter equation, cosθ(c)=f(1)cosθ(1)-f(2), with f(1)+f(2)≥1, should be used. The differences between the two equations are discussed and the errors involved in using the incorrect equation are estimated to be between ~3° and 13° for superhydrophobic surfaces. The discrepancies between the two equations are also discussed for the case of a liquid undergoing partial, but increasing, levels of penetration. Finally, a general equation is presented for the transition/stability criterion between the Cassie-Baxter and Wenzel modes of wetting.     

Proficiency testing in analytical laboratories: how to make it work

 This paper covers the role of proficiency testing schemes in providing an occasional but objective means of assessing and documenting the reliability of the data produced by a laboratory, and in encouraging the production of data that are "fit-for-purpose". A number of aspects of proficiency testing are examined in order to highlight features critical for their successful implementation. Aspects that are considered are: accreditation, the economics and scope of proficiency testing schemes, methods of scoring, assigned values, the target value of standard deviation σ_p, the homogeneity of the distributed material, proficiency testing in relation to other quality assurance measures and whether proficiency testing is effective. Stress is placed on the importance of any proficiency testing scheme adhering to a protocol that is recognised, preferably internationally. It is also important that the results from the scheme are transparent to both participating laboratory and its "customer". Received: 03 November 1995 Accepted: 20 November 1995     

Extended floating spherical Gaussian basis sets for Molecules. FSGO basis for use in advanced correlated calculations of electronic structures

The transformation of occupied and excited SCF orbitals expressed in Cartesian Gaussian form to a smaller, simpler set of floating spherical Gaussians is described. Illustrative applications at the correlated coupled-cluster level are presented for Lill and H₂O.     

Projection between basis sets: A means of defining the electronic structure of functional subunits

The general problem of the transfer of the representation of a set of orthonormal functions from one basis to a different, nonequivalent one is considered and specialized to a matrix formulation convenient for use in molecular electronic structure calculations. A procedure is suggested for treating problems where the transfer of representation breaks into a subset of most interest and one of less interest as for example the occupied and virtual orbitals of a Hartree-Fock SCF calculation. These techniques are then applied to obtain a representation of a methyl group from an SCF wave function for methane.     

Numerical Hartree-Fock and MCSCF calculations on diatomic copper: calibration of basis sets

NHF and NMCSCF results for Cu₂ are compared with calculations employing basis set expansions. We find that nearly all previous SCF calculations using Gaussian basis sets have underestimated the bond length by about the same amount (0.03 Å) as that attributed to the unlinked cluster and relativistic corrections. The error is shown to be due to deficiencies in the 3d primitive set which yield sizable basis set superposition errors.     

The electronic structure and one-electron properties of BH computed from SCF and CI wave functions

The SCF and CI wave functions for BH, obtained in calculations described in detail elsewhere [2], are compared through their electron distributions and electron moments.Taken in part from a Ph.D. thesis submitted to the University of Toronto in 1971.     

Molecular structure and electronic spectrum of taspine: Semiempirical calculations

AM1 calculations show that taspine has the three energy-minima along the rotation-like nuclear displacement of the dimethylaminoethyl group. They correspond to two enantiomeric structures and a Cs structure, which have nearly equal energies. The energy barrier between the enantiomeric structures and the Cs structure is calculated to be about 1 kcal/mol. The small barrier readily causes an intramolecular interconversion of the two enantiomers through the Cs structure and thus results in the optical inactivity of taspine. CNDO/S calculations show that the electronic spectra of the enantiomer and the Cs structure are quite similar. These calculated spectra are in good agreement with the observed electronic spectra.     

Extrapolation to the limit of a complete basis set for electronic structure calculations on the N2 molecule

Results obtained from nonrelativistic electronic structure calculations using finite Gaussian basis sets are extrapolated to the limit of a complete basis set, employing the results of explicitly correlated coupled-cluster calculations including singles and doubles substitutions (CCSD). For N₂, the basis-set limits for the electronic binding energy, equilibrium bond length and harmonic vibrational wave number are established for the CCSD model including a perturbative correction for triples substitutions and for the internally contracted multireference configuration interaction method. The resulting numbers are in good agreement with experimental values. Received: 2 December 1997 / Accepted: 3 February 1998 / Published online: 17 June 1998     

The high-valent iron-oxo species of polyoxometalate, if it can be made, will be a highly potent catalyst for C-H hydroxylation and double-bond epoxidation

This study uses density functional theory (DFT) calculations to explore the reactivity of the putative high-valent iron-oxo reagent of the iron-substituted polyoxometalate (POM-FeO4-), derived from the Keggin species, PW12O40(3-). It is shown that POM-FeO4- is in principle capable of C-H hydroxylation and C=C epoxidation and that it should be a powerful oxidant, even more so than the Compound I species of cytochrome P450. The calculations indicate that in a solvent, the barriers, and especially those for epoxidation, become sufficiently small that one may expect an extremely fast reaction. An experimental investigation (by R.N. and A.M.K.) shows, however, that the formation of POM-FeO4- using the oxygen donor, F5PhI-O, leads to a persistent adduct, POM-FeO-I-PhF5(4-), which does not decompose to POM-FeO4- + F5Ph-I at the working temperature and exhibits sluggish reactivity, in accord with previous experimental results (Hill, C. L.; Brown, R. B., Jr. J. Am. Chem. Soc. 1986, 108, 536 and Mansuy, D.; Bartoli, J.-F.; Battioni, P.; Lyon, D. K.; Finke, R. G. J. Am. Chem. Soc. 1991, 113, 7222). Subsequent calculations indeed reveal that the gas-phase binding energy of F5PhI to POM-FeO4- is high (ca. 20 kcal/mol) compared to the corresponding binding energy of propene (ca. 2-3 kcal/mol). As such, the POM-FeO-I-PhF5(4-) complex is expected to be persistent toward the displacement of F5PhI by a substrate like propene, leading thereby to sluggish oxidative reactivity. According to theory, overcoming this technical difficulty may turn out to be very rewarding. The question is, can POM-FeO4- be made?     

Accurate quantum-chemical calculations using Gaussian-type geminal and Gaussian-type orbital basis sets: applications to atoms and diatomics

We have implemented the use of mixed basis sets of Gaussian one- and two-electron (geminal) functions for the calculation of second-order M?ller-Plesset (MP2) correlation energies. In this paper, we describe some aspects of this implementation, including different forms chosen for the pair functions. Computational results are presented for some closed-shell atoms and diatomics. Our calculations indicate that the method presented is capable of yielding highly accurate second-order correlation energies with rather modest Gaussian orbital basis sets, providing an alternative route to highly accurate wave functions. For the neon atom, the hydrogen molecule, and the hydrogen fluoride molecule, our calculations yield the most accurate MP2 energies published so far. A critical comparison is made with established MP2-R12 methods, revealing an erratic behaviour of some of these methods, even in large basis sets.     

Compact basis sets for LCAO-LSD calculations. Part I: Method and bases for Sc to Zn

A method for preparing compact orbital and auxiliary basis sets for LCAO-LSD calculations has been developed. The method has been applied to construct basis sets for first row transition metal atoms from Sc to Zn for the 3d^n?14s¹ and 3d^n?24s² configurations. The properties of different expansion patterns have been tested in atomic calculations for the chromium atom.     

The electronic structures of HCP and FCP: A comparison of the results of SCF calculations with several different basis sets,and the inclusion of electron correlation

Ab initio calculations using a variety of basis sets and including electron correlation via the MP3 method are reported for HCP and FCP and their positive ions. Comparisons are made with the available experimental data.N.F.C.R Postgraduate Student.     

Continuum electrostatics for electronic structure calculations in bulk amorphous polymers: application to polylactide

The bond rotational energy landscapes of polylactide (PLA) oligomers were estimated using electron density functional theory (DFT) at the B3LYP/6-31G** level, both in vacuo and with a self-consistent reaction field (SCRF) method to simulate the electronic environment within the condensed phase. The SCRF method was evaluated for application to polymeric systems, and we demonstrate the difficulties involved in applying the method to bulk amorphous polymers with specific attention to the selection of the solvent probe radius. In addition, rotational isomeric states (RIS) calculations were performed, showing the effect of accounting for the bulk phase reaction field on the bond rotational energetics and characteristic ratio. We conclude that present methods of accounting for bulk environments in electronic structure calculations are not well suited for use with polymeric systems, and the development of improved methods is needed in this area.     

The electronic structure of carbon suboxide from ESCA and AB initio calculations

The ESCA spectrum of C₃O₂ excited by Mg K_α radiation, 1253.6 eV, has been obtained for both gaseous and solid samples. The chemical shifts of the C1s and O1s levels have been used to calculate the gross atomic charges. The valence region of the spectrum has been recorded and the ordering of the orbitals has been decided on the basis of an ab initio calculation and the intensities of the observed peaks. An unusually intense shake-up spectrum has also been observed and is discussed. The relative spacing of the valence peaks has been found to be different for the solid and gas.