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Journal articles on the topic 'Molecular integrals'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 September 2024

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1

Matsuoka, Osamu. "Molecular integrals over Laguerre Gaussian-type functions of real spherical harmonics." Canadian Journal of Chemistry 70, no. 2 (February 1, 1992): 388–92. http://dx.doi.org/10.1139/v92-055.

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Molecular integrals are formulated over the Laguerre Gaussian-type functions (LGTF) of real spherical harmonics. They include the overlap integrals and the energy integrals of kinetic, nuclear attraction, and electron repulsion. For the nuclear-attraction integrals the formulations based on the point as well as the Gaussian nuclear charge distribution models are presented. Integral formulas over the LGTFs of real spherical harmonics are found a little more complicated than those of the LGTFs of complex spherical harmonics due to the summations over magnetic quantum numbers. Keywords: molecular integral, Gaussian-type function, spherical harmonic, solid harmonic, Sonine polynomial.

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2

Barnett, Michael P. "Mathscape and molecular integrals." Journal of Symbolic Computation 42, no. 3 (March 2007): 265–89. http://dx.doi.org/10.1016/j.jsc.2006.07.002.

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3

Dawass, Noura, Peter Krüger, Sondre K. Schnell, Othonas A. Moultos, Ioannis G. Economou, Thijs J. H. Vlugt, and Jean-Marc Simon. "Kirkwood-Buff Integrals Using Molecular Simulation: Estimation of Surface Effects." Nanomaterials 10, no. 4 (April 16, 2020): 771. http://dx.doi.org/10.3390/nano10040771.

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Kirkwood-Buff (KB) integrals provide a connection between microscopic properties and thermodynamic properties of multicomponent fluids. The estimation of KB integrals using molecular simulations of finite systems requires accounting for finite size effects. In the small system method, properties of finite subvolumes with different sizes embedded in a larger volume can be used to extrapolate to macroscopic thermodynamic properties. KB integrals computed from small subvolumes scale with the inverse size of the system. This scaling was used to find KB integrals in the thermodynamic limit. To reduce numerical inaccuracies that arise from this extrapolation, alternative approaches were considered in this work. Three methods for computing KB integrals in the thermodynamic limit from information of radial distribution functions (RDFs) of finite systems were compared. These methods allowed for the computation of surface effects. KB integrals and surface terms in the thermodynamic limit were computed for Lennard–Jones (LJ) and Weeks–Chandler–Andersen (WCA) fluids. It was found that all three methods converge to the same value. The main differentiating factor was the speed of convergence with system size L. The method that required the smallest size was the one which exploited the scaling of the finite volume KB integral multiplied by L. The relationship between KB integrals and surface effects was studied for a range of densities.

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4

Chang, Chia-En, Michael J. Potter, and Michael K. Gilson. "Calculation of Molecular Configuration Integrals." Journal of Physical Chemistry B 110, no. 13 (April 2006): 7083. http://dx.doi.org/10.1021/jp061244u.

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5

Chang, Chia-En, Michael J. Potter, and Michael K. Gilson. "Calculation of Molecular Configuration Integrals." Journal of Physical Chemistry B 107, no. 4 (January 2003): 1048–55. http://dx.doi.org/10.1021/jp027149c.

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6

Barnett, Michael P. "Molecular integrals over slater orbitals." Chemical Physics Letters 166, no. 1 (February 1990): 65–70. http://dx.doi.org/10.1016/0009-2614(90)87051-r.

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7

Barnett, Michael P. "Molecular integrals and information processing." International Journal of Quantum Chemistry 95, no. 6 (2003): 791–805. http://dx.doi.org/10.1002/qua.10614.

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8

Rico, J. Fernández, R. López, and G. Ramírez. "Molecular integrals with Slater basis. III. Three‐center nuclear attraction integrals." Journal of Chemical Physics 94, no. 7 (April 1991): 5032–39. http://dx.doi.org/10.1063/1.460538.

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9

Murphy, Kevin V., Justin M. Turney, and Henry F. Schaefer. "Student-Friendly Guide to Molecular Integrals." Journal of Chemical Education 95, no. 9 (July 19, 2018): 1572–78. http://dx.doi.org/10.1021/acs.jchemed.8b00255.

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10

Fern�ndez Rico, J., R. L�pez, G. Ram�rez, and J. I. Fern�ndez-Alonso. "Auxiliary functions for Slater molecular integrals." Theoretica Chimica Acta 85, no. 1-3 (March 1993): 101–7. http://dx.doi.org/10.1007/bf01374580.

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11

Dawass, Noura, Peter Krüger, Sondre K. Schnell, Jean-Marc Simon, and T. J. H. Vlugt. "Kirkwood-Buff integrals from molecular simulation." Fluid Phase Equilibria 486 (May 2019): 21–36. http://dx.doi.org/10.1016/j.fluid.2018.12.027.

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12

YU. ORLOV, A. "NEW SOLVABLE MATRIX INTEGRALS." International Journal of Modern Physics A 19, supp02 (May 2004): 276–93. http://dx.doi.org/10.1142/s0217751x04020476.

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We generalize the Harish-Chandra-Itzykson-Zuber and certain other integrals (the Gross-Witten integral, the integrals over complex matrices and the integrals over rectangle matrices) using a notion of the tau function of the matrix argument. In this case one can reduce multi-matrix integrals to integrals over eigenvalues, which in turn are certain tau functions. We also consider a generalization of the Kontsevich integral.

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13

Bouferguene, A., M. Fares, and D. Rinaldi. "Integrals overBfunctions basis sets. I. Three‐center molecular integrals, a numerical study." Journal of Chemical Physics 100, no. 11 (June 1994): 8156–68. http://dx.doi.org/10.1063/1.466810.

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14

Fernández Rico, J., R. López, G. Ramírez, and C. Tablero. "Molecular integrals with Slater basis. V. Recurrence algorithm for the exchange integrals." Journal of Chemical Physics 101, no. 11 (December 1994): 9807–16. http://dx.doi.org/10.1063/1.467946.

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15

Koch, Wolfhard, Bastian Freyb, Juan Francisco Sánchez Ruiza, and Thomas Scior. "On the Restricted and Combined Use of Rüdenberg’s Approximations in Molecular Orbital Theories of Hartree-Fock Type." Zeitschrift für Naturforschung A 58, no. 12 (December 1, 2003): 756–84. http://dx.doi.org/10.1515/zna-2003-1212.

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Rüdenberg’s well-known letter of 1951 entitled “On the Three- and Four-Center Integrals in Molecular Quantum Mechanics” explicitly presents two approximation formulas for four-center repulsion integrals, only. When applied to some types of three-center repulsion integrals, however, these two recipes still imply considerable oversimplifications. Using both one-electron and two-electron routes of Rüdenberg’s truncated expansion, on the other hand, such shortcomings can be avoided strictly. Starting from four simple “Unrestricted and Combined” (U&C) approximation schemes introduced elsewhere, an improved “Restricted and Combined” (R&C) approximation picture for Fock-matrix elements now will be outlined, which does not tolerate any unnecessary oversimplifications. Although the simplicity of the U&C scheme is lost in this case, R&C-approximated Fock-matrix elements still can be constructed from one- and two-center integrals alone in an effective way. Moreover, due to their dependence on a single geometric parameter, all types of two-center integrals can be calculated in advance for about one hundred fixed interatomic distances at the desired level of sophistication and stored once and for all. A cubic spline algorithm may be taken to interpolate the actual integral value from each precomputed list.

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16

Hu, Anguang, and Brett I. Dunlap. "Three-center molecular integrals and derivatives using solid harmonic Gaussian orbital and Kohn–Sham potential basis sets." Canadian Journal of Chemistry 91, no. 9 (September 2013): 907–15. http://dx.doi.org/10.1139/cjc-2012-0485.

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Three-center integrals over Gaussian orbital and Kohn–Sham (KS) basis sets are reviewed. An orbital basis function carries angular momentum about its atomic center. That angular momentum is created by solid harmonic differentiation with respect to the center of an s-type basis function. That differentiation can be brought outside any purely s-type integral, even nonlocal pseudopotential integrals. Thus the angular factors associated with angular momentum and differentiation with respect to atom position can be pulled outside loops over orbital and KS Gaussian exponents.

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17

Carbó, Ramon, and Emili Besalú. "AO integral evaluation using Cartesian exponential type orbitals (CETOs)." Canadian Journal of Chemistry 70, no. 2 (February 1, 1992): 353–61. http://dx.doi.org/10.1139/v92-050.

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CETO functions and their properties are defined and described, to provide a means of obtaining general expressions for many-center many-electron integral formulae. Compact integral expressions are written by means of nested summation symbols, a new concept developed in this paper. Integrals over CETO functions are computed by means of a set of several auxiliary integral forms. No transformations other than frame rotations are needed to compute the usual integral terms. The formulae obtained are immediately programmable in any high level language and the parallelizable terms are obtained with a simple rule. Results can be considered an encouraging alternative way to solve the STO integral problem. Keywords: many-center AO integrals, molecular basis sets, ETO, STO, CETO.

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18

HONDA, Hiroaki, and Shigeru OBARA. "Molecular Integrals Evaluated over Contracted Gaussian Functions." Journal of Computer Chemistry, Japan 4, no. 4 (2005): 165–74. http://dx.doi.org/10.2477/jccj.4.165.

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19

Glaesemann, Kurt R., and Laurence E. Fried. "Quantitative molecular thermochemistry based on path integrals." Journal of Chemical Physics 123, no. 3 (July 15, 2005): 034103. http://dx.doi.org/10.1063/1.1954771.

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20

Krack, Matthias, and Andreas M. Köster. "An adaptive numerical integrator for molecular integrals." Journal of Chemical Physics 108, no. 8 (February 22, 1998): 3226–34. http://dx.doi.org/10.1063/1.475719.

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21

Bhattacharya, A. K., and S. C. Dhabal. "Molecular overlap integrals with exponential‐type orbitals." Journal of Chemical Physics 84, no. 3 (February 1986): 1598–605. http://dx.doi.org/10.1063/1.450453.

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22

Tai, H. "Analytic evaluation of two-center molecular integrals." Physical Review A 33, no. 6 (June 1, 1986): 3657–66. http://dx.doi.org/10.1103/physreva.33.3657.

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23

Wedberg, Rasmus, John P. O'Connell, Günther H. Peters, and Jens Abildskov. "Accurate Kirkwood–Buff integrals from molecular simulations." Molecular Simulation 36, no. 15 (December 2010): 1243–52. http://dx.doi.org/10.1080/08927020903536366.

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24

Avery, John Scales, and James Emil Avery. "Rapid evaluation of molecular integrals with ETOs." International Journal of Quantum Chemistry 115, no. 15 (May 10, 2015): 930–36. http://dx.doi.org/10.1002/qua.24924.

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25

Berlu, Lilian, and Philip Hoggan. "Useful Integrals for Ab-Initio Molecular Quantum Similarity Measurements Using Slater Type Atomic Orbitals." Journal of Theoretical and Computational Chemistry 02, no. 02 (June 2003): 147–61. http://dx.doi.org/10.1142/s0219633603000513.

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Molecular quantum similarity measurements are based on a quantitative comparison of the one-electron densities of two molecules superposed and aligned to optimize a well-defined similarity function. In most previous work the densities have been related using a Dirac delta leading to the overlap-like quantum similarity function. The densities for the two molecules compared have generally been approximated often with a simple LCAO of s-gaussian functions. In this work, we present a one center two range expansion method for the evaluation of the overlap integrals involved in the overlap-like quantum similarity function over Slater type orbitals (STO). The single center and three types of two-center overlap integrals (involving four atomic orbitals; two in each molecule) have led to finite sums using a single center approach combined with selection rules obtained by analysis of orbital angular momentum (conservation). The three- and four-center integrals are also obtained analytically but involve infinite sums which require further study before leading to a complete set of integral codes for ab-initio quantum similarity.

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26

LAPORTA, S. "ANALYTICAL EXPRESSIONS OF THREE- AND FOUR-LOOP SUNRISE FEYNMAN INTEGRALS AND FOUR-DIMENSIONAL LATTICE INTEGRALS." International Journal of Modern Physics A 23, no. 31 (December 20, 2008): 5007–20. http://dx.doi.org/10.1142/s0217751x08042869.

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In this paper we continue the work began in 2002 on the identification of the analytical expressions of Feynman integrals which require the evaluation of multiple elliptic integrals. We rewrite and simplify the analytical expression of the three-loop self-mass integral with three equal masses and on-shell external momentum. We collect and analyze a number of results on double and triple elliptic integrals. By using very high-precision numerical fits, for the first time we are able to identify a very compact analytical expression for the four-loop on-shell self-mass integral with four equal masses, that is one of the master integrals of the four-loop electron g-2. Moreover, we fit the analytical expressions of some integrals which appear in lattice perturbation theory, and in particular the four-dimensional generalized Watson integral.

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27

Guseinov, Israfil, Bahtiyar Mamedov, and Afet Rzaeva. "Calculation of molecular integrals over Slater-type orbitals using recurrence relations for overlap integrals and basic one-center Coulomb integrals." Journal of Molecular Modeling 8, no. 4 (April 1, 2002): 145–49. http://dx.doi.org/10.1007/s00894-002-0079-8.

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28

Maksić, Z. B. "Some Molecular Integrals over Ellipsoidal Hermite-Gaussian Functions." Zeitschrift für Naturforschung A 41, no. 7 (July 1, 1986): 921–27. http://dx.doi.org/10.1515/zna-1986-0704.

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Some molecular integrals over ellipsoidal Hermite-Gaussian functions relevant for SCF calculations are considered. It is shown that all integrals can be expressed in a closed form if the H nzA (axAXA) H nyA (ayA yA) H nzA (azA zA) exp (-br2A basis set is employed. It appears also that this type of functions is convenient for the calculation of electric properties of molecules. Finally, a relation between the H G and harmonic oscillator functions is established.

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29

BERLU, LILIAN, and HASSAN SAFOUHI. "ANALYTICAL TREATMENT OF NUCLEAR MAGNETIC SHIELDING TENSOR INTEGRALS OVER EXPONENTIAL-TYPE FUNCTIONS." Journal of Theoretical and Computational Chemistry 07, no. 06 (December 2008): 1215–25. http://dx.doi.org/10.1142/s0219633608004374.

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The present work concerns the analytical and numerical development of three-center molecular integrals over Slater-type functions (STFs) and B functions of the second order involving [Formula: see text] in the operator. These integrals appear in the analytic expression of the nuclear magnetic shielding tensor. The basis set of STFs is used to represent atomic orbitals. These STFs are expressed in terms of B functions, which are better suited to apply the Fourier transform method thoroughly developed by Steinborn group. Analytic expressions are obtained for the integrals of the second order involved in nuclear magnetic resonance shielding tensor over B functions. These expressions turned out to be similar to those obtained for the usual molecular multi-center integrals. Consequently, the numerical evaluation of the integrals under consideration will benefit from the work previously done on the molecular multi-center integrals.

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30

Kuang, Jiyun, and C. D. Lin. "Molecular integrals over spherical Gaussian-type orbitals: I." Journal of Physics B: Atomic, Molecular and Optical Physics 30, no. 11 (June 14, 1997): 2529–48. http://dx.doi.org/10.1088/0953-4075/30/11/007.

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31

Fernández Rico, J., R. López, and G. Ramírez. "Molecular integrals with Slater basis. I. General approach." Journal of Chemical Physics 91, no. 7 (October 1989): 4204–12. http://dx.doi.org/10.1063/1.456799.

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32

Matsuoka, Osamu. "Molecular integrals over spherical Laguerre Gaussian‐type functions." Journal of Chemical Physics 92, no. 7 (April 1990): 4364–71. http://dx.doi.org/10.1063/1.457744.

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33

Ishida, Kazuhiro. "Molecular integrals over the gauge-including atomic orbitals." Journal of Chemical Physics 118, no. 11 (March 15, 2003): 4819–31. http://dx.doi.org/10.1063/1.1545776.

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34

Barnett, Michael P. "Digital erosion in the evaluation of molecular integrals." Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta) 107, no. 4 (April 1, 2002): 241–45. http://dx.doi.org/10.1007/s00214-002-0322-5.

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35

Persson, B. Joakim, and Peter R. Taylor. "Molecular integrals over Gaussian-type geminal basis functions." Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta) 97, no. 1-4 (October 13, 1997): 240–50. http://dx.doi.org/10.1007/s002140050258.

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36

Lindh, Roland, Per-Åke Malmqvist, and Laura Gagliardi. "Molecular integrals by numerical quadrature. I. Radial integration." Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta) 106, no. 3 (July 1, 2001): 178–87. http://dx.doi.org/10.1007/s002140100263.

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37

Jensen, Jan H. "Modeling intermolecular exchange integrals between nonorthogonal molecular orbitals." Journal of Chemical Physics 104, no. 19 (May 15, 1996): 7795–96. http://dx.doi.org/10.1063/1.471485.

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38

Fortunelli, Alessandro, and Oriano Salvetti. "Overlapping and non-overlapping integrals in molecular calculations." Chemical Physics Letters 186, no. 4-5 (November 1991): 372–78. http://dx.doi.org/10.1016/0009-2614(91)90194-e.

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39

Maslen, E. N., and M. G. Trefry. "Two-center molecular repulsion integrals over slater functions." International Journal of Quantum Chemistry 37, no. 1 (January 1990): 51–68. http://dx.doi.org/10.1002/qua.560370105.

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40

Lu, Yannan, and Zuqia Huang. "Molecular integrals in the generalized hylleraas-CI method." International Journal of Quantum Chemistry 38, no. 3 (September 1990): 447–60. http://dx.doi.org/10.1002/qua.560380307.

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41

Ha, Tae-Kyu, William H. Fink, and Leland C. Allen. "Multicenter distribution of molecular integrals and energy components." International Journal of Quantum Chemistry 1, S1 (June 18, 2009): 431–43. http://dx.doi.org/10.1002/qua.560010648.

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42

Rico, J. Fernández, R. López, and G. Ramírez. "Molecular integrals with Slater basis. IV. Ellipsoidal coordinate methods for three‐center nuclear attraction integrals." Journal of Chemical Physics 97, no. 10 (November 15, 1992): 7613–22. http://dx.doi.org/10.1063/1.463481.

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43

Guseinov, I. I., R. Aydin, and B. A. Mamedov. "Computation of molecular integrals over Slater-type orbitals. III. Calculation of multicenter nuclear-attraction integrals using recurrence relations for overlap integrals." Journal of Molecular Structure: THEOCHEM 503, no. 3 (May 2000): 173–77. http://dx.doi.org/10.1016/s0166-1280(99)00284-5.

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44

Guseinov, I. I., B. A. Mamedov, and R. Aydin. "Computation of molecular integrals over Slater-type orbitals. IV. Calculation of multicenter electron-repulsion integrals using recurrence relations for overlap integrals." Journal of Molecular Structure: THEOCHEM 503, no. 3 (May 2000): 179–88. http://dx.doi.org/10.1016/s0166-1280(99)00285-7.

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45

Largo-Cabrerizo, A., C. Urdaneta, G. C. Lie, and E. Clementi. "The Hylleraas-CI integrals in molecular, calculations. II. Three-and four-electron integrals and tests for two-electron many-center integrals." International Journal of Quantum Chemistry 32, S21 (March 12, 1987): 677–92. http://dx.doi.org/10.1002/qua.560320767.

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46

Fernández Rico, Jaime, Guillermo Ramírez, Rafael López, and José I. Fernández-Alonso. "Accurate gaussian expansion of STO's. Test of many-center slater integrals." Collection of Czechoslovak Chemical Communications 53, no. 10 (1988): 2250–65. http://dx.doi.org/10.1135/cccc19882250.

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The use of large STO-NG expansions for testing algorithms and procedures designed for the calculation of many-center molecular integrals with Slater basis functions was previously proposed. Expansions up to the STO-12G for the 1s and 2s cases and a method for calculating integrals involving higher quantum numbers were there reported. Here, we present the corresponding expansions from STO-13G to STO-27G. Further tests on the convergence in the integral calculations with the new expansions are also included and the results are compared with those obtained previously. These new expansions are necessary when highly accurate comparisons are required.

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47

Lovrod, Jordan, and Hassan Safouhi. "Computing Four-Center Two-Electron Coulomb Integrals Using Exponential Transformations and Trapezoidal Rule." EPJ Web of Conferences 226 (2020): 01009. http://dx.doi.org/10.1051/epjconf/202022601009.

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The numerical evaluations of the four-center two-electron Coulomb integrals are among the most time-consuming computations involved in molecular electronic structure calculations. In the present paper we extend the double exponential (DE) transform method, previously developed for the numerical evaluation of threecenter one-electron molecular integrals [J. Lovrod, H. Safouhi, Molecular Physics (2019) DOI:10.1030/0026867.2019.1619854], to four-center two-electron integrals. The fast convergence properties analyzed in the numerical section illustrate the advantages of the new approach.

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48

BRACKEN, PAUL. "AN ABELIAN MODEL OF GRAVITY AND CANONICAL QUANTIZATION BY MEANS OF PATH INTEGRALS." International Journal of Modern Physics A 25, no. 26 (October 20, 2010): 4901–10. http://dx.doi.org/10.1142/s0217751x10050676.

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An Abelian model of gravity is introduced and its constraint structure is obtained. The main task is to show that the model with constraints can be canonically quantized by means of the canonical path integral formalism using the Faddeev–Popov approach. It is shown how the path integral can be simplified by carrying out the integrals over those variables for which the integrals can be computed.

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49

Guseinov, I. I., and B. A. Mamedov. "Computation of molecular integrals over Slater type orbitals I. Calculations of overlap integrals using recurrence relations." Journal of Molecular Structure: THEOCHEM 465, no. 1 (May 1999): 1–6. http://dx.doi.org/10.1016/s0166-1280(98)00129-8.

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50

Righi, A. F. M., and C. A. Kuhnen. "Molecular Orbitals Calculation on LiH with Algebraic Treatment of the Integrals." International Journal of Modern Physics C 08, no. 05 (October 1997): 1159–68. http://dx.doi.org/10.1142/s0129183197001028.

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In this work we employ an algebraic computational method to solve the integrals which arise in the study of diatomic molecules. Using the Slater-type orbitals (STO), we obtain analytical solutions for the one-center and two-center hybrid and Coulomb integrals. The exchange integrals are considered, as much as possible, in a similar manner. These results are used to calculate the electronic properties of the ground state of the LiH molecule, by means of a variational calculation using a basis of molecular orbitals. The behavior of the Slater exponents of the atomic orbitals are studied as functions of internuclear distance. We show that the STO undergo a lengthening of their shape when the nuclear separation increases.

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