Calculation of molecular integrals over Slater-type orbitals using recurrence relations for overlap integrals and basic one-center Coulomb integrals

The recurrence relations are established for the basic one-center Coulomb integrals over Slater-type orbitals (STOs). These formulae and the recurrence relations for basic overlap integrals are utilized for the calculation of multicenter electron-repulsion integrals. The calculations of multicenter electron-repulsion integrals are performed by the use of translation formulae for STOs obtained from the Lambda and Coulomb Sturmian exponential-type functions (ETFs). It is shown that these integrals show a faster convergence rate in the case of Coulomb Sturmian ETFs. The accuracy of the results is quite high for the quantum numbers of STOs and for the arbitrary values of internuclear distances and screening constants of atomic orbitals.     

Addition theorems for Slater-type orbitals and their application to multicenter multielectron integrals of central and noncentral interaction potentials

By the use of complete orthonormal sets of psi(alpha)-ETOs (alpha=1, 0, m1, m2,...) introduced by the author, new addition theorems are derived for STOs and arbitrary central and noncentral interaction potentials (CIPs and NCIPs). The expansion coefficients in these addition theorems are expressed through the Gaunt and Gegenbauer coefficients. Using the addition theorems obtained for STOs and potentials, general formulae in terms of three-center overlap integrals are established for the multicenter t-electron integrals of CIPs and NCIPs that arise in the solution of the N-electron atomic and molecular problem (2hthN) when a Hylleraas approximation in Hartree-Fock-Roothaan theory is employed. With the help of expansion formulae for translation of STOs, the three-center overlap integrals are expressed through the two-center overlap integrals. The formulae obtained are valid for arbitrary quantum numbers, screening constants and location of orbitals.     

Addition theorems for Slater-type orbitals in momentum space and their application to three-center overlap integrals

Using addition theorems for complete orthonormal sets of exponential type orbitals in the momentum representation introduced by the author, the addition theorems are established for Slater type orbitals in momentum space. With the help of these addition theorems, the general series expansion formulae in terms of the product of two-center overlap integrals are established for the three-center overlap integrals that arise in the solution of atomic and molecular problems occurring when explicitly correlated methods are employed. The formulae obtained for addition theorems and three-center overlap integrals are valid for arbitrary location and parameters of orbitals.     

Calculation of multicenter electric field gradient integrals over Slater-type orbitals using unsymmetrical one-range addition theorems

The electric field induced within a molecule by its electrons determines a whole series of important physical properties of the molecule. In particular, the values of the gradient of this field at the nuclei determine the interaction of their quadrupole moments with the electrons. Using unsymmetrical one-range addition theorems introduced by one of the authors, the sets of series expansion relations for multicenter electric field gradient integrals over Slater-type orbitals in terms of multicenter charge density expansion coefficients and two-center basic integrals are presented. The convergence of the series is tested by calculating concrete cases for different values of quantum numbers, parameters and locations of orbitals.     

Computation of multicenter overlap integrals with Slater-type orbitals using Ψ<Superscript>α</Superscript>-ETOs

Multicenter overlap integrals appearing in the evaluation of multicenter–multielectron integrals of central and noncentral interaction potentials are calculated using complete orthonormal sets of -ETOs (=1, 0, –1, –2, ...). The final results are expressed in terms of two-center overlap integrals between STOs. The convergence of the series is tested by calculating concrete cases for arbitrary quantum numbers, screening constants and location of STOs.     

Theoretical CD studies of polypeptide helices: examination of important electronic and geometric factors

An improved model for calculating the CD of polypeptides has been developed. Excited state wavefunctions were derived from CNDO/S (complete neglect of differential overlap, spectroscopic) calculations on N-methylacetamide. Four discrete peptide-localized transitions were employed: pi 0 pi* (NV1), pi* + pi* (NV2), n pi*, and n' pi*. Inclusion of the pi + pi transition (lambda 0 = 140 nm) significantly improves the accuracy of the calculated CD spectra in the 180-250-nm region. Spectra were computed for various helical structures, including right-handed alpha-, alpha II-, omega-, pi-, 3(10-), and poly (proline) I-helices, and the left-handed poly (proline) II-helix. Sensitivity to changes in the peptide backbone geometry and chain length are examined. Electronic factors such as ground-state charge distribution, hybridization effects, and basis set deorthogonalization have been investigated. The nonconservative nature of the poly (Pro) I and II CD spectra is reproduced, and the helix band present in earlier exciton calculations on the alpha-helix has been diminished.     

Use of Ψ<Superscript>α</Superscript>-ETOs in the unified treatment of electronic attraction,electric field and electric field gradient multicenter integrals of screened Coulomb potentials over Slater orbitals

In this study, using complete orthonormal sets of -ETOs (where =1, 0, –1, –2, ...)introduced by the author, a large number of series expansion formulae for the multicenter electronic attraction (EA), electric field (EF) and electric field gradient (EFG) integrals of the Yukawa-like screened Coulomb potentials (SCPs) is presented through the new central and noncentral potentials and the overlap integrals with the same screening constants. The final results obtained are valid for arbitrary locations of STOs and their parameters.An erratum to this article can be found at     

Difficulties in parentage analysis: the probability that an offspring and parent have the same heterozygous genotype.

Parentage studies often estimate the number of parents contributing to half-sib progeny arrays by counting the number of alleles attributed to unshared parents. This approach is compromised when an offspring has the same heterozygous genotype as the shared parent, for then the contribution of the unshared parent cannot be unambiguously deduced. To determine how often such cases occur, formulae for co-dominant markers with n alleles are derived here for Ph, the probability that a given heterozygous parent has an offspring with the same heterozygous genotype, and Pa, the probability that a randomly chosen offspring has the same heterozygous genotype as the shared parent. These formulae have been derived assuming Mendelian segregation with either (1) an arbitrary mating system, (2) random mating or (3) mixed mating. The maximum value of Pa under random mating is 0.25 and occurs with any two alleles each at a frequency of 0.5. The behaviour with partial selfing (where reproduction is by selfing with probability s, and random mating otherwise) is more complex. For n < or = 3 alleles, the maximum value of Pa occurs with any two alleles each at a frequency of 0.5 if s < 0.25, and with three equally frequent alleles otherwise. Numerically, the maximum value of Pa for n > or = 4 alleles occurs with n* < or = n alleles at equal frequencies, where the maximizing number of alleles n* is an increasing function of the selfing rate. Analytically, the maximum occurs with all n alleles present and equally frequent if s > or = 2/3. In addition, the potential applicability of these formulae for evolutionary studies is briefly discussed.     

Comment on “numerical treatment of two-center overlap integrals”

The subject paper by H. Safouhi (J Mol Model 12:213–220, 2006) presents a scheme based on a nonlinear convergence acceleration transformation for the numerical evaluation of two-center overlap integrals of Slater-type orbitals. In this comment we argue that there is no reason to adopt such an approach, as well-known methods for these integrals are substantially superior both in speed and in accuracy.     

UV photoelectron spectroscopy and ab initio characterization of valence orbital structures and conformations of neutral phosphate esters

The HeI UV photoelectron spectrum of trimethyl phosphate (TMP) has been measured and interpreted with the aid of SCF molecular orbital calculations carried out with STO-3G, STO-3G* and 4-31G basis functions. The photoelectron spectrum of TMP is more accurately reproduced by results from 4-31G calculations than by results from STO-3G or STO-3G* calculations. However, all three basis sets yield results which predict the same assignment of the photoelectron spectrum. Results at the 4-31G level indicate that whether calculations are based on crystallographic bond angles and bond lengths or on STO-3G optimized geometries has little effect on the energetic ordering of the upper occupied orbitals. The energetic ordering of orbitals is also found to be only weakly dependent upon the torsional angle phi, describing rotation of ester groups about P-O bonds and upon the torsional angle psi, describing rotation of methyl groups about C-O bonds. For trimethyl phosphate, with C3 symmetry, the vertical ionization potentials of the upper occupied orbitals are 10.81 eV (8e), 11.4 eV (9a), 11.93 eV (7e), 12.6-12.9 eV (8a and 6e), 14.4 eV (7a) and 15.0-16.0 eV (5e and 6a). Calculations at the 4-31G level indicate that many of the highest occupied orbitals in neutral dimethyl phosphate and methyl phosphate have energies and electron distributions similar to orbitals in TMP. For TMP, a search for optimized values of phi and psi has been carried out at the STO-3G*level. In agreement with previous NMR studies and with classical potential calculations, the STO-3G* results indicate that both the gauche (phi = 53.1 degrees) and anticlinal (phi = 141.9 degrees) conformations are thermally accessible. Also in agreement with the classical potential calculations, the STO-3G* results predict that in the all gauche conformation energy is minimized when the methyl groups assume a staggered geometry (psi = 60 degrees to 80 degrees) and that an energy maximum occurs for an eclipsed geometry (phi = 0 degrees to 20 degrees). A study of the dependence of optimized values of O-P-O ester bond angles on the torsional angles, phi, was carried out at the STO-3G, STO-3G* and 4-31G levels. The results demonstrate that for C3 symmetry, the coupling of O-P-O angles to phi is influence by repulsive steric interactions.     

UV Photoelectron Spectroscopy and Ab Initio Characterization of Valence Orbital Structures and Conformations of Neutral Phosphate Esters

Abstract

The Hel UV photoelectron spectrum of trimethyl phosphate (TMP) has been measured and interpreted with the aid of SCF molecular orbital calculations carried out with STO-3G, STO-3G* and 4–31G basis functions. The photoelectron spectrum of TMP is more accurately reproduced by results from 4–31G calculations than by results from STO-3G or STO-3G* calculations. However, all three basis sets yield results which predict the same assignment of the photoelectron spectrum. Results at the 4–31G level indicate that whether calculations are based on crystallographic bond angles and bond lengths or on STO-3G optimized geometries has little effect on the energetic ordering of the upper occupied orbitals. The energetic ordering of orbitals is also found to be only weakly dependent upon the torsional angle φ, describing rotation of ester groups about P-O bonds and upon the torsional angle ψ, describing rotation of methyl groups about C-O bonds. For trimethyl phosphate, with C₃ symmetry, the vertical ionization potentials of the upper occupied orbitals are 10.81 eV (8e), 11.4 eV (9a), 11.93 eV (7e), 12.6–12.9 eV (8a and 6e), 14.4 eV (7a) and 15.0–16.0 eV(5e and 6a). Calculations at the 4–31G level indicate that many of the highest occupied orbitals in neutral dimethyl phosphate and methyl phosphate have energies and electron distributions similar to orbitals in TMP.

For TMP, a search for optimized values of φ and ψ has been carried out at the STO-3G* level. In agreement with previous NMR studies and with classical potential calculations, the STO- 3G* results indicate that both the gauche φ= 53.1 °) and anticlinal (φ = 141.9°) conformations are thermally accessible. Also in agreement with the classical potential calculations, the STO-3G* results predict that in the all gauche conformation energy is minimized when the methyl groups assume a staggered geometry (ψ= 60° to 80°) and that an energy maximum occurs for an eclipsed geometry (ψ = 0° to 20°). A study of the dependence of optimized values of O-P-O ester bond angles on the torsional angles, φ, was carried out at the STO-3G, STO-3G* and 4–31G levels. The results demonstrate that for C₃ symmetry, the coupling of O-P-O angles to φ is influenced by repulsive steric interactions.     

Kinetic and spectral parameters of the amines oxidative N-dealkylation with participation of the liver microsomal cytochrome P-450. Amines oxidation with organic hydroperoxides

Kinetics of demethylation of a number of amines involving hepatic microsomal cytochrome P-450 and organic hydroperoxides (tret-butyl- and cumylhydroperoxide) have been investigated. Decomposition rate constants for the substrate-cytochrome P-450-ROOH complexes have been determined in a generalized form. Activation parameters, deltaH* and deltaS*, are calculated for decomposition of the complexes. There is a linear relation between deltaH* and deltaS*: deltaH*=18.7 kcal + 333 degrees K deltaS*. Compensation relationship is characterized by the value of alpha=333 degrees K/Taverage=1.11. The nature of the limiting step in the cytochrome P-450-NADPH-O2-system and the cytochrome P-450-ROOH-system is discussed.     

The quaternary structure of the sheaths of defective phages similar to PBS X.

The contractile sheaths of five defective, PBS X-like bacteriophages from Bacillus subtilis and B. licheniformis were investigated by electron microscopy, dodecylsulphate gel electrophoresis and immunodiffusion. Electron microscope images of the extended and contracted sheaths were of similar appearance, although their lengths were different. The surface lattices of both the extended and the contracted sheaths were determined by optical diffraction. This showed that the quaternary structure of the sheaths of all five defective phages originated from identical surface lattices, which could be approximately expressed by the selection rules L = -2n' + 3m and L = 9N' + 17M for the extended and contracted sheaths respectively, in which 6n' = n with n = 0 or an integer multiple of 6. These results indicated that the packing of the protein subunits in these sheaths differed from those of other bacteriophages, for example T4 and millimicron [Amos and Klug, J. Mol. Biol. 99, 51--73 (1975); Admiraal and Mellema, J. Ultrastruct. Res. 56, 48--64 (1976)]. The molecular weight of the main sheath protein of the defective phages, as determined by dodecylsulphate gel electrophoresis, was approximately 50000. This value differed from that for T4, but was similar to that of millimicron [Admiraal and Mellema, J. Ultrastruct. Res. 56, 48--64 (1976); King and Laemmli, J. Mol. Biol, 75, 315--337 (1973)]. The results of immunodiffusion experiments, however, pointed to a chemical difference between the sheath proteins of the defective phages and millimicron, in addition to T4.     

Addition and expansion theorems for complete orthonormal sets of exponential-type orbitals in coordinate and momentum representations

Analytical properties of new complete orthonormal sets of Psi(alpha) exponential-type orbitals (Psi(alpha)-ETOs where alpha=1, 0, -1, -2, em leader ), introduced by the author as finite linear combinations of Slater-type orbitals (STOs), are studied. Addition and expansion theorems for Psi(alpha)-ETOs are obtained in both coordinate and momentum representations. Using expressions of Psi(alpha)-ETOs in terms of STOs, the new methods are suggested to calculate multicenter multielectron integrals over STOs.     

山西产9种野生植物的染色体观察

本文报道了产于山西的4科5属9种野生植物的染色体观察结果。其中有2种植物作了核型分析,5种植物的染色体为首次报道。     

Kinetics of N-dealkylation of amines with participation of microsomal cytochrome P-450]

Within the temperature range of 20-37 degrees C the kinetics of the demethylation reactions of a variety of amines with participation of hepatic microsomal cytochrome P-450, NADPH and O2 has been studied. Catalytical rate constants for all the substrates have been determined in generalized forms. Activation parameters deltaH* and deltaS* are also estimated. There is a linear relationship between deltaH* and deltaS*: deltaH*=20.7 kcal+366 degrees K deltaS*. Compensation relationship is characterized by a coefficient alpha=366 degrees/Taverage=1.21. The nature of the limiting step of the enzymatic amine demethylation involving cytochrome P-450 of hepatic microsomes is discussed.     

东北蒿属莳萝蒿组6种植物核型研究

报道东北蒿属莳萝蒿组６种植物的染色体数,５种为首次报道,对其中的５种进行了核型分析。核型公式分别为：大籽蒿２ｎ＝２ｘ＝１８＝１４ｍ＋２ｓｍ（２ＳＡＴ）＋２ｓｔ（ＳＡＴ）;矮滨蒿（Ａ．ｎａｋａｉ Ｐａｍｐ）２ｎ＝２ｘ＝１６＝１２ｍ＋４ｓｍ;碱蒿（Ａ．ａｎｅｔｈｉｆｏｌｉａ Ｗｅｂ．ｅｘ Ｓｔｅｃｈｍ．）２ｎ＝２ｘ＝１６＝１２ｍ＋２ｓｍ＋２ｓｔ;莳萝蒿（Ａ．ａｎｅｔｈｏｉｄｅｓ Ｍａｔｔｆ）２ｎ＝２ｘ     

两种蒿属植物的染色体数目和核型研究

本文报道了我国蒿属2个种的染色体核型,它们的核型模式为:油蒿2n=36=28m+6sm+2st;褐沙蒿2n=36=26m+2sm+8st(2SAT)。     

Frontier molecular orbital analysis of Cu(n)-O(2) reactivity

Frontier molecular orbital (FMO) theory coupled with density functional calculations has been applied to investigate the chemical reactivity of three key bioinorganic Cu(n)-O(2) complexes, the mononuclear end-on hydroperoxo-Cu(II), the side-on bridged mu-eta(2):eta(2)-O(2)(2-) Cu(II)(2) dimer and the bis-mu-oxo Cu(III)(2) dimer. Two acceptor orbitals (sigma* and pi*) of each complex and two types of donating substrates (sigma-substrate, phosphine; pi-substrate, alkylbenzene) are considered in the electrophilic attack mechanism. The angular dependences of different reaction pathways are determined using FMO theory and the angular overlap model. Including steric effects, the sigma*/sigma and pi*/pi pathways are found more reactive than the corresponding cross sigma*/pi and pi*/sigma pathways which have poor donor-acceptor orbital overlaps in the sterically constrained substrate access region.     

Europium-labeled melanin-concentrating hormone analogues: ligands for measuring binding to melanin-concentrating hormone receptors 1 and 2

We investigated the use of Eu3+ chelate-labeled analogues of melanin-concentrating hormone (MCH) as ligands for both human MCH receptors (MCHR1 and MCHR2). The analogues employed were Ala17 MCH, S36057 (Y-ADO-RC*MLGRVFRPC*W, where ADO=8-amino-3,6-dioxyoctanoyl and *=disulfide bond), and R2P (RC*MLGRVFRPC*Y-NH2). The peptides were readily labeled on the alpha-amino residue with the Eu3+ chelate of N1-(p-isothiocyanatobenzyl)-diethylenetriamine-N1,N2,N3,N3-tetraacetic acid and then purified by reverse-phase fast-performance liquid chromatography at neutral pH to maintain Eu3+ chelation. Both labeled Ala17 MCH and S36057 had high affinity for MCHR1 ( Kd = 0.37 and 0.059nM, respectively) while Eu3+ -labeled S36057 and R2P had high affinity for MCHR2 ( Kd = 0.16 and 0.10nM, respectively). Labeled Ala17 MCH had little demonstrable binding affinity for MCHR2. Eu3+ -labeled S36057 and R2P were full agonists at MCHR1 when assessed by measurement of agonist-stimulated GTPgamma(35)S binding. Competition binding experiments with both MCHR isoforms, a series of previously characterized alanine scan MCH analogues, and a recently identified nonpeptide MCHR1-selective antagonist T-226296 confirmed the expected receptor selectivity. These studies further extend the utility of Eu3+ chelate time-resolved fluorescence for the development of high-sensitivity, nonradioactive receptor binding assays and demonstrate the need to select the optimal ligand for labeling.