Molecular integrals over Gaussian-type geminal basis functions

We present formulas for the evaluation of molecular integrals over basis functions with an explicit Gaussian dependence on interelectronic coordinates. These formulas use expansions in Hermite Gaussian functions and represent an extension to the work of McMurchie and Davidson to two-electron basis functions. Integrals that depend on the coordinates of up to four electrons are discussed explicitly. A key feature of this approach is that it allows full exploitation of the shell structure of the orbital part of the basis. Received: 24 February 1997 / Accepted: 4 March 1997     

Electronic structure of BeH2

Nonorthogonal single‐configuration and multiconfiguration ab initio calculations are carried out on the BeH₂ molecule in its equilibrium (D_∞h) geometry, using a highly optimized even‐tempered Slater‐type orbital (STO) basis set. The results are used as a basis for a discussion of the electronic structure of the molecule in modern‐VB terms. A value of R_e = 1.329 Å is obtained. Values are also obtained for the symmetric‐stretch harmonic frequency (2053 cm^?1), electric quadrupole moment (?5.60 Buckingham), and nuclear quadrupole coupling constants (?3.59 MHz for ⁹Be and 0.0915 MHz for ²H). © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Detection of single nucleotide polymorphisms using electrospray ionization mass spectrometry: validation of a one-well assay and quantitative pooling studies

Single nucleotide polymorphisms (SNPs) are currently being mapped and databased at a remarkable pace, providing a viable means for understanding disease susceptibility, differential drug response and human evolution. Consequently, there is an increasing demand for SNP genotyping technologies that are simple, rapid, cost effective and readily amenable to automation for high-throughput analyses. In this study, we improved the Survivor Assay, a SNP detection method based on electrospray ionization mass spectrometry (ESI-MS), with several developments. One improvement is the development of a one-well assay, requiring no off-line purification of the polymerase chain reaction product, achieved by simple addition of reagent solution into a single well. Another is the on-line separation of magnesium and dideoxynucleotides using an in-house made monolithic metal chelating column, eliminating any off-line sample preparation prior to mass spectrometric analysis. Here the Survivor Assay is extended from a proof-of-principle concept to a validated method by genotyping six SNPs from five different regions of human genomic DNA in 55 individual samples with 100% accuracy. This improved Survivor Assay eliminates the tedious and time-consuming steps of sample preparation, minimizes sample handing and offers a high-throughput analysis of SNPs by ESI-MS. The current combined preparation and analysis time is 2 min per sample. The simplicity of this method has potential for full automation and parallel chromatography and, thus, reduced analysis time. In addition, we have adapted the Survivor Assay for quantitative SNP analysis in pooled DNA samples. The capabilities and sensitivity of this approach were evaluated. We demonstrate that an allele occurring at a frequency of 2% can consistently be quantitated.     

Reduced-size polarized basis sets for calculations of molecular electric properties. IV. First-row transition metals

Recent studies of the perturbation-dependent basis sets have indicated the possibility of a significant reduction of the size of the usual CGTO sets without considerable loss of accuracy in calculations of molecular electric properties. The resulting (ZPolX) basis sets have been developed for several atoms of the first and second row of the Periodic Table. The same method of the ZPolX basis set generation is extended for the first-row transition metals and the corresponding contracted ZPolX basis sets of the size [6s5p3d1f] are determined for both nonrelativistic and scalar relativistic calculations. The performance of the ZPolX basis sets is verified in calculations on the first-row transition metal oxides at the level of the ROHF, ROHF/CASPT2, and ROHF/CCSD(T) approximations. Also the study of the dipole polarizability of TiCl₄ confirms the excellent features of these very compact basis sets. The ZPolX basis sets for nonrelativistic and relativistic calculations of molecular electric properties are available on the web page http://www.chem.uni.torun.pl/zchk/basis-sets.html.     

The convergence of the Rayleigh-Ritz Method in quantum chemistry

Two sufficient criteria for the convergence of the Rayleigh-Ritz Method (RRM) with respect to the eigenvalues (E-convergence) of non-relativistic electronic Hamiltonians of molecules are discussed and compared. Moreover, a necessary and sufficient criterion is given. By example (Sect. 9) it is shown that the L ²-completeness of the basis is not sufficient to guarantee E-convergence. The convergence of the wave functions in different norms (-convergence) is also investigated. In particular, sufficient conditions for the one-particle basis functions (orbitals) are given, such that a CI calculation in this basis is both E- and -convergent.     

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     

Medium-size Gaussian basis sets for hydrogen through argon

Summary Medium-sized Gaussian basis sets are reoptimized for the ground states of the atoms from hydrogen through argon. The composition of these basis sets is (4s), (5s), and (6s) for H and He, (9s5p) and (12s7p) for the atoms Li to Ne, and (12s8p) and (12s9p) for the atoms Na to Ar. Basis sets for the² P states of Li and Na, and the³ P states of Be and Mg are also constructed since they are useful in molecular calculations. In all cases, our energies are lower than those obtained previously with Gaussian basis sets of the same size.     

Basis Set Orbital Relaxation in Atomic and Molecular Hydrogen Systems

Orbital relaxation (OR) amounts to variation of the orbital exponents in hydrogen molecules and ions relative to the exponents of the isolated atom; it is represented as the sum of the one- and two-center contributions depending on the effective atomic charge and on the presence of other atoms in the molecule. The procedure for isolating the contributions of the exponent includes treatment of the OR of hydrogen in a special set of neutral and charged atoms and molecules with certain multiplicities of their electronic states. Within the framework of the spin-unrestricted Hartree-Fock method, we found and discussed the optimal values of the exponents of the basis orbitals of hydrogen atoms and molecules using the minimal split valence-shell basis set, the basis set that includes the polarization function, and the expanded set of grouped natural orbitals. A simple energy model is suggested for OR. Expressions are derived for evaluating the exponents of the relaxed orbitals in hydrogen-containing systems.Original Russian Text Copyright © 2004 by A. I. Ermakov, A. E. Merkulov, A. A. Svechnikova, and V. V. Belousov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 973–978, November–December, 2004.     

Complete basis set ab initio computational study of ionization potential, electron affinity and the C-F bond dissociation energy for perfluorinated methane derivatives

A computational study of perfluorinated methane derivatives was performed with complete basis set ab initio methods. The total energies for their neutral, cation, and anionic states were computed. From these values, the energy gaps between different electronic states, ionization potentials, electron affinities, and C-F bond dissociation energies were calculated. The computed values are compared with experimental data and the reliability of complete basis set ab initio methods is discussed. New values for C-F bond dissociation energies are suggested. Received: 12 January 1998 / Accepted: 2 April 1998 / Published online: 29 July 1998     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The first-order polarized basis sets for the use in high-level-correlated investigations of molecular electric properties have been generated for Pb, Bi, Po, and At. The performance of the standard [10.17.14.5/13.11.8.2] and extended [20.17.14.9/13.11.8.4] basis sets has been examined in nonrelativistic and quasirelativistic calculations for atoms and simple closed-shell hydrides. The relativistic contributions to electric dipole properties of those systems have been evaluated by using the recently developed quasirelativistic scheme. The predicted dipole polarizability of At is in good agreement with the results of other relativistic calculations. The calculated quasirelativistic dipole moments of BiH₃ (–0.499 a.u.), PoH₂ (–0.207 a.u.), and AtH (+0.036 a.u.) involve a significant relativistic contribution which amounts to —0.230 a.u., –0.177 a.u., and –0.097 a.u., respectively. The basis set details append this paper. They are also available as a part of the basis set library of the MOLCAS system.