Correlation Effects on ππ* Transition Energies in the Series of Linear Polyenes. II. σπ Correlation Effects in the Minimal Basis Set

1970 ◽  
Vol 52 (9) ◽  
pp. 4769-4774 ◽  
Author(s):  
Armelle Denis ◽  
J. P. Malrieu
Keyword(s):  
Basis Set ◽  
Correlation Effects ◽  
Minimal Basis ◽  
Transition Energies ◽  
Linear Polyenes

scholarly journals Pentagon functions for scattering of five massless particles

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
D. Chicherin ◽  
V. Sotnikov
Keyword(s):  
Phase Space ◽  
Numerical Evaluation ◽  
Public Library ◽  
Basis Set ◽  
Particle Scattering ◽  
Minimal Basis ◽  
Feynman Integrals ◽  
Analytic Expressions ◽  
Transcendental Functions ◽  
Branch Cuts

Abstract We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space. We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts. We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications.

Nonnuclear Maxima in the Charge Density

1993 ◽  
Vol 48 (1-2) ◽  
pp. 127-133 ◽  
Author(s):  
Kenneth E. Edgecombe ◽  
Vedene H. Smith, Jr. ◽  
Florian Müller-Plathe
Keyword(s):  
Charge Density ◽  
Electron Density ◽  
Electron Correlation ◽  
Basis Set ◽  
Valence Shell ◽  
Correlation Effects ◽  
Electron Correlation Effects

Abstract Basis-set and electron-correlation effects on the appearance and disappearance of nonnuclear maxima in the electron density are examined in Li2 , Na2 , Na4 and Na5 . It is shown that nonnuclear attractors can be removed in all cases except Li2 . The appearance of a pseudoatom in a lithium molecule correlates remarkably well with the size of the region, in an atomic calculation, of V2r(r) for the valence shell of the atom. This and the fact that the pseudoatom is also present in the promolecule indicate that the pseudoatoms are remnants of, or in fact are portions of, atoms that are not perturbed enough in the molecule to remove an essentially atomic characteristic.

Calculation of electrostatic potentials and fields inside zeolite cavities

1988 ◽  
Vol 53 (10) ◽  
pp. 2308-2319 ◽  
Author(s):  
János G. Ángyán ◽  
György Ferenczy ◽  
Péter Nagy ◽  
Gábor Náray-Szabó
Keyword(s):  
Ab Initio ◽  
Lone Pair ◽  
Electrostatic Potentials ◽  
Basis Set ◽  
Mean Deviation ◽  
Minimal Basis ◽  
Approximate Methods ◽  
Monopole Approximation ◽  
Van Der Waals Surface ◽  
Modified Formula

We present a modification of our bond increment method for the calculation of molecular electrostatic potentials and fields inside zeolite cavities. Introducing a variant of the Mulliken approximation for the off-diagonal matrix elements of the potential and optimizing the parameters of the modified formula, we achieved much better agreement with ab initio STO-3G minimal basis set results than with the original version. For a representative set of 10 small molecules the standard mean deviation between potentials calculated on the van der Waals surface with the ab initio and approximate methods is 9·1 kJ/mol. The relative error decreases from 21 to 9 per cent for the lone-pair regions of molecules modelling zeolite cavities. Applying the modified bond increment method for a realistic faujausite model we have found that the potential and field are almost exclusively of long-range origin. This means that, if using appropriate atomic charges, the monopole approximation gives correct results for electrostatic potentials and fields inside zeolite cavities.

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