The characteristic polynomials of structures with pending bonds

It is well known [1] that the calculation of characteristic polynomials of graphs of interest in Chemistry which are of any size is usually extremely tedious except for graphs having a vertex of degree 1. This is primarily because of numerous combinations of contributions whether they were arrived at by non-imaginative expansion of the secular determinant or by the use of some of the available graph theoretical schemes based on the enumeration of partial coverings of a graph, etc. An efficient and quite general technique is outlined here for compounds that have pending bonds (i.e., bonds which have a terminal vertex). We have extended here the step-wise pruning of pending bonds developed for acyclic structures by one of the authors [2] for elegant evaluation of the characteristic polynomials of trees by accelerating this process, treating pending group as a unit. Further, it is demonstrated that this generalized pruning technique can be applied not only to trees but to cyclic and polycyclic graphs of any size. This technique reduces the secular determinant to a considerable extent. The present technique cannot handle only polycyclic structures that have no pending bonds. However, frequently such structures can be reduced to a combination of polycyclic graphs with pending bonds [3] so that the present scheme is applicable to these structures too. Thus we have arrived at an efficient and quite a simple technique for the construction of the characteristic polynomials of graphs of any size.     

Calculating multidimensional discrete variable representations from cubature formulas

Finding multidimensional nondirect product discrete variable representations (DVRs) of Hamiltonian operators is one of the long standing challenges in computational quantum mechanics. The concept of a "DVR set" was introduced as a general framework for treating this problem by R. G. Littlejohn, M. Cargo, T. Carrington, Jr., K. A. Mitchell, and B. Poirier (J. Chem. Phys. 2002, 116, 8691). We present a general solution of the problem of calculating multidimensional DVR sets whose points are those of a known cubature formula. As an illustration, we calculate several new nondirect product cubature DVRs on the plane and on the sphere with up to 110 points. We also discuss simple and potentially very useful finite basis representations (FBRs), based on general (nonproduct) cubatures. Connections are drawn to a novel view on cubature presented by I. Degani, J. Schiff, and D. J. Tannor (Num. Math. 2005, 101, 479), in which commuting extensions of coordinate matrices play a central role. Our construction of DVR sets answers a problem left unresolved in the latter paper, namely, the problem of interpreting as function spaces the vector spaces on which commuting extensions act.     

Gegenbauer polynomials in a theoretical study of the vibrational structure of the Ca+–H2 system

This work presents an application of Gegenbauer polynomials in vibrational calculations. We illustrated that by example calculations of vibrational structure of the Ca⁺–H₂ exciplex, in the state correlated with 3D calcium ion state. For this case Gegenbauer polynomials are used for formation of a basis set for a bending mode. We showed that this basis set leads to a faster convergence of results than a basis set formed from Legendre polynomials. Additionally we compared vibrational structure obtained in this manner with results of discrete variable representation-distributed Gaussian basis (DVR–DGB) method.     

The small planarization barriers for the amino group in the nucleic acid bases

The amino group in the nucleic acid bases frequently interacts with other bases or with other molecular systems. Thus any nonplanarity of the amino group may affect the molecular recognition of nucleic acids. Ab initio Hartree-Fock (HF) and second-order Moller-Plesset perturbation (MP2) levels of theory have been used to obtain the equilibrium geometries of the C(l) and C(s) structures for five common nucleic acid bases. The energy barriers between the C(l) and C(s) structures have also been predicted. A series of correlation consistent basis sets up to cc-pCVQZ and aug-cc-pVQZ has been used to systematically study the dependence of the amino group nonplanarity. The equilibrium geometries of the nucleic acid bases with an amino group, including adenine, guanine, and cytosine, are examined carefully. At the MP2 level of theory, larger basis sets decrease the extent of nonplanarity of the amino group, but the decrease slows down when the QZ basis sets are used, demonstrating the intrinsic property of nonplanarity for guanine. For adenine and cytosine the situation is less clear; as the HF limit is approached, these two structures become planar. Addition of core correlation effects or diffuse functions further decreases the degree of nucleic acid base nonplanarity, in comparison to the original cc-pVXZ (X=D, T, and Q) basis sets. The aug-cc-pVXZ basis shows smaller degrees of nonplanarity than the cc-pCVXZ sets. The aug-cc-pVXZ basis is less size dependent than the cc-pVXZ and cc-pCVXZ sets in the prediction of the amino-group-related bond angles and dihedral angles and energy barriers for adenine, guanine, and cytosine. The cc-pCVQZ and aug-cc-pVQZ MP2 results may be regarded as benchmark predictions for the five common bases. The predicted classical barriers to planarization are 0.02 (adenine), 0.74 (guanine), and 0.03(cytosine) kcal mol(-1).     

New analytical expressions,symmetry relations and numerical solutions for the rotational overlap integrals

In this article, extremely simple analytical formulas are obtained for rotational overlap integrals which occur in integrals over two reduced rotation matrix elements. The analytical derivations are based on the properties of the Jacobi polynomials and beta functions. Numerical results and special values for rotational overlap integrals are obtained by using symmetry properties and recurrence relationships for reduced rotation matrix elements. The final results are of surprisingly simple structures and very useful for practical applications. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Linear scaling computation of the Fock matrix. VII. Periodic density functional theory at the Gamma point

Linear scaling quantum chemical methods for density functional theory are extended to the condensed phase at the Gamma point. For the two-electron Coulomb matrix, this is achieved with a tree-code algorithm for fast Coulomb summation [M. Challacombe and E. Schwegler, J. Chem. Phys. 106, 5526 (1997)], together with multipole representation of the crystal field [M. Challacombe, C. White, and M. Head-Gordon, J. Chem. Phys. 107, 10131 (1997)]. A periodic version of the hierarchical cubature algorithm [M. Challacombe, J. Chem. Phys. 113, 10037 (2000)], which builds a telescoping adaptive grid for numerical integration of the exchange-correlation matrix, is shown to be efficient when the problem is posed as integration over the unit cell. Commonalities between the Coulomb and exchange-correlation algorithms are discussed, with an emphasis on achieving linear scaling through the use of modern data structures. With these developments, convergence of the Gamma-point supercell approximation to the k-space integration limit is demonstrated for MgO and NaCl. Linear scaling construction of the Fockian and control of error is demonstrated for RBLYP6-21G* diamond up to 512 atoms.     

Consistent gaussian basis sets of double‐ and triple‐zeta valence with polarization quality of the fifth period for solid‐state calculations

Consistent basis sets of double‐ and triple‐zeta valence with polarization quality for the fifth period have been derived for periodic quantum‐chemical solid‐state calculations with the crystalline‐orbital program CRYSTAL. They are an extension of the pob‐TZVP basis sets, and are based on the full‐relativistic effective core potentials (ECPs) of the Stuttgart/Cologne group and on the def2‐SVP and def2‐TZVP valence basis of the Ahlrichs group. We optimized orbital exponents and contraction coefficients to supply robust and stable self‐consistent field (SCF) convergence for a wide range of different compounds. The computed crystal structures are compared to those obtained with standard basis sets available from the CRYSTAL basis set database. For the applied hybrid density functional PW1PW, the average deviations of calculated lattice constants from experimental references are smaller with pob‐DZVP and pob‐TZVP than with standard basis sets. © 2018 Wiley Periodicals, Inc.     

Discrete analogs of spherical harmonics and their use in quantum mechanics: The hyperquantization algorithm

Summary An algorithm for the solution of the Schrödinger equation in a discrete basis is illustrated with reference to the problem of quantization on spheres of any dimension (hyperquantization). It exploits the explicit construction of discrete analogs of spherical harmonics and leads to sparse matrix representations of the kinetic energy operator and a diagonal representation of the interaction potential. Applications are discussed for inelastic and reactive scattering.     

乙醛二聚体的从头计算

用ab initio分子轨道法在STO-3G和6-31G水平上, 全构型优化, 对二聚乙醛的各种稳定构型进行了研究。结果表明, 在STO/6-31G水平上, 最稳定的乙醛二聚体为具有对称中心的环状结构, 包含由醛基氢和醛基氧组成的二个C—H…O氢键。结合能为-20.17 kJ·mol~(-1), 与实验估计的结合能-22.39±0.15 kJ·mol~(-1)比较接近。STO-3G过低估计了乙醛二聚体的结合能, 在不同构型的相对稳定性方面也与6-31G不一致。     

Program for analyzing knots represented by polygonal paths

Knots can occur in real and model biological macromolecules. We describe a program for determining whether or not any knots are present in model structures and for classifying those knots that do occur. The program computes the Alexander polynomial, Δ(t), for any model. This polynomial characterizes the knot in the sense that if two knots have different Alexander polynomials, then the knots are topologically distinct. The Alexander polynomial of the circle, or trivial knot, is Δ(t)≡1. If the computed Alexander polynomial is not identically equal to unity, then the structure is nontrivially knotted, and the program will then determine a lower bound on the minimum number of path crossings. The program is entirely general, and may be used to analyze any closed polygonal path. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 813–818, 1999     

Some further considerations on deriving matrix elements of non-periodic potentials in the basis of the non-degenerate harmonic oscillator wavefunctions

Using the properties of the generating function of the Hermite polynomials, we have calculated the matrix elements for the Gaussian-type potential V_G(x)=A exp{−B(x−C)²} and for the Morse-type potential V_M(x)=D_e[1−exp(−ax)]² in the basis of the non-degenerate harmonic oscillator wavefunctions. The final forms of these matrix elements are very simple to use and hence suitable for the numerical resolution of the Schrödinger equation for multiple-well potentials or anharmonic oscillators.     

Consistent Gaussian basis sets of triple‐zeta valence with polarization quality for solid‐state calculations

Consistent basis sets of triple‐zeta valence with polarization quality for main group elements and transition metals from row one to three have been derived for periodic quantum‐chemical solid‐state calculations with the crystalline‐orbital program CRYSTAL. They are based on the def2‐TZVP basis sets developed for molecules by the Ahlrichs group. Orbital exponents and contraction coefficients have been modified and reoptimized, to provide robust and stable self‐consistant field (SCF) convergence for a wide range of different compounds. We compare results on crystal structures, cohesive energies, and solid‐state reaction enthalpies with the modified basis sets, denoted as pob‐TZVP, with selected standard basis sets available from the CRYSTAL basis set database. The average deviation of calculated lattice parameters obtained with a selected density functional, the hybrid method PW1PW, from experimental reference is smaller with pob‐TZVP than with standard basis sets, in particular for metallic systems. The effects of basis set expansion by diffuse and polarization functions were investigated for selected systems. © 2012 Wiley Periodicals, Inc.     

Substituent effects on the binding of natural product anthocyanidin inhibitors to influenza neuraminidase with mass spectrometry

The binding of three closely related anthocyanins within the 430-cavity of influenza neuraminidase is studied using a combination of mass spectrometry and molecular docking. Despite their similar structures, which differ only in the number and position of the hydroxyl substituents on the phenyl group attached to the chromenylium ring, subtle differences in their binding characteristics are revealed by mass spectrometry and molecular docking that are in accord with their inhibitory properties by neuraminidase inhibition assays. The cyanidin and delphinidin, with the greatest number of hydroxyl groups, bind more strongly and are better inhibitors than pelargonidin that contains a lone hydroxyl group at the 4′ position. The study demonstrates, for the first time, the sensitivity of the mass spectrometry based approach for investigating the molecular basis and relative affinity of antiviral inhibitors, with subtly different structures, to their target protein. It has broader application for the screening of other protein interactions more generally with reasonable high-throughput.     

Thermochemical properties of polycyclic aromatic hydrocarbons (PAH) from G3MP2B3 calculations

In this article, we present a new database of thermodynamic properties for polycyclic aromatic hydrocarbons (PAH). These large aromatic species are formed in very rich premixed flames and in diffusion flames as part of the gas-phase chemistry. PAH are commonly assumed to be the intermediates leading to soot formation. Therefore, accurate prediction of their thermodynamic properties is required for modeling soot formation. The present database consists of 46 species ranging from benzene (C6H6) to coronene (C24H12) and includes all the species usually present in chemical mechanisms for soot formation. Geometric molecular structures are optimized at the B3LYP/6-31++G(d,p) level of theory. Heat capacity, entropy, and energy content are calculated from these optimized structures. Corrections for hindered rotor are applied on the basis of torsional potentials obtained from second-order M?ller-Plesset perturbation (MP2) and Dunning's consistent basis sets (cc-pVDZ). Enthalpies of formation are calculated using the mixed G3MP2//B3 method. Finally, a group correction is applied to account for systematic errors in the G3MP2//B3 computations. The thermodynamic properties for all species are available in NASA polynomial form at the following address: http://www.stanford.edu/group/pitsch/.     

Light-dependent isomeric effects of polycyclic aromatic hydrocarbons on the predication of DNA cleavage factor efficiency

PAHs, short for polycyclic aromatic hydrocarbons, are a ubiquitous group of chemically related, environmentally persistent organic compounds having diverse structures and varied toxicity. They have been shown to cause mutagenic and carcinogenic effects on organisms and are quite immunosuppressive. Time-dependent density functional theory (TD-DFT) offers a practical means of understanding the behavior of excitation energies for PAHs. Here, we examined the performance of the long-range corrected Coulomb-attenuating functional (CAM-B3LYP) in relation to four different basis sets, determining which basis set compliments the functional better in identifying the most reactive atomic site on six isomeric PAH compounds. Condensed Fukui function indices were used to compare the performance of applied basis sets in identifying the most reactive atomic site on six isomeric PAHs compounds, assessing which basis set would be more appropriate in determining the site where free-radical formation would occur after light irradiation. Dunning’s correlation consistent triple-zeta (cc-pVTZ) basis set was determined to have the best PAH characterization performance, concluding the need for application of a higher-level basis set with the long-range corrected Coulomb-attenuating functional. Although each compound was a structural isomer of the other, the reactive atomic sites varied for each molecule with the use of an applied basis set. It was concluded that structural shape has some influence on the calculation of PAH characteristics. Lastly, in order to predict DNA single-stranded cleavage factor for the compounds proposed here, we have used the quantitative structure-activity relationship (QSAR). The cleavage factor values for the set of aromatic molecules with similar structures have been collected from the literature for a total number of 22 compounds.     

An ab initio comparison of dichalcogen hydrides

A theoretical study of HSH, HSeH, HTeH, HSSH, HSeSH, HSeSeH, HTeSH, HTeSeH, and HTeTeH was carried out by ab initio molecular orbital methods employing minimal Gaussian basis sets MINI-1 and MINI-1* of Huzinaga and his group. Both basis sets yield accurate estimates on the equilibrium geometries of monochalcogen hydrides. In the case of dichalcogen hydrides, however, the inclusion of d-polarization functions for sulfur, selenium, and tellurium greatly improve the accuracy of the geometry prediction. The unpolarized MINI-1 basis sets yield essentially correct orbital energies and therefore suffice for the comparative study on the electronic structures in similar molecules. The results with both basis sets imply close similarities in the electronic structures of SS, SeS, and SeSe bonds with more marked differences in bonds containing tellurium as a consequence of notably smaller orbital energy of the 5s- orbital of tellurium as compared to the corresponding orbitals in sulfur and selenium. The barriers to internal rotation about the chalcogen—chalcogen bond in all dichalcogen hydrides are similar. The cis- and trans-barrier heights are ca. 23 and 14 kJ mol⁻¹, respectively. The relative stabilities of different hydrides are discussed.     

Structure and electronic properties of ladder polymers. A new class of conducting polymers

Theoretical calculations have been applied to design novel synthetic polymers which show metallic conductivity without doping. Some selected highly conjugated structures were calculated using a HUCKELMO method extended by introducing elastic sigma bonds. A group of highly conjugated aromatic ladder polymers is promising in this context. Another interesting group consists of laddered heteroaromatic structures in which carbon atoms are replaced by nitrogen. Ionization potentials, electron affinities, band widths, band gaps as well as oxidation and reduction potentials were calculated. Small, band gaps were obtained for polyacene, polyperinaphthalene and polypyridinopyridine. The values are in good aggreement with that obtained on the basis of the VEH method. This paper reports also some efforts to prepare polyacene, polyperinaphthalene and polypyridinopyridine, and to investigate their electronic properties. Concerning their electrochemical properties high specific capacities and good electrochemical stability has been found in aprotic lithium cells.     

Pseudo-two-dimensional structures (HXYH)3n2H6n (XY = GaN, SiC, GeC, SiSi, or GeGe; n = 1-3): density functional characterization of structures and energetics

Hybrid density functional calculations with effective core potential basis sets are performed for monomeric group 13/15 and group 14/14 analogues of cyclohexane, as well as for three different pseudo-two-dimensional structures that can be formed from expanding one and two concentric rings around the central one (trans-fused chairs, a rolling combination of trans- and cis-fused chairs, and cis-fused boats). Varying contributions from torsional strain, angle strain, electrostatics, and nontraditional H-H hydrogen bonding lead to different orderings and magnitudes of motif energies in the various systems: Homoatomic SiSi and GeGe systems prefer the trans-fused chair alternative and heteroatomic systems GaN, SiC, and GeC prefer the rolling chair. Decomposition of structure energies into characteristic fragment contributions indicates that pseudo-one-dimensional rods of poly(imidogallane) are thermodynamically more stable than any of the pseudo-two-dimensional structures.     

Crystal structures of 2- and 3-cyanopyridine

The crystals of 2- and 3-cyanopyridine isomers have been obtained by a sublimation method. The crystal structures of both isomers have been determined on the basis of low-temperature X-ray single crystal experiments and compared, also in relation to 4-cyanopyridine. In 2-cyanopyridine the nitrogen atom of the CN group, whereas in 3- the N-ring atom, is involved in the shortest intermolecular contact. In both cases, the hydrogen bond type interactions are rather of a weak nature, but they are important for developing of the polymeric chains.     

2-isoxazoline derivatives—VIII : The reaction of nitrile oxides with tropone

The reaction of nitrile oxides with tropone yields a mixture of at least 8 products, the structures of which are based on spectral and chemical evidence. Both addition of the 1,3-dipole to the carbonyl group and cycloadditions to the CC double bonds system have been observed. Peri-, regio- and stereo-selectivity of the 1,3-dipole cycloaddition are discussed and rationalized on the basis of simple perturbation theory approach.