Calculations of molecular polarizabilities from electric-field-variant atomic orbitals: An analysis of the problem and its application to the hydrogen molecule and to the alkane series

It is shown how an aufbau principle for atoms arises from the Hartree-Fock (HF) treatment with increasing numbers of electrons. The Slater screening rules are introduced. The HF equations for general molecules are not separable in the spatial variables. This requires another approximation, such as the linear combination of atomic orbitals (LCAO) molecular orbital method. The orbitals of molecules are represented in a basis set of known functions, for example atomic orbital (AO)-like functions or plane waves. The HF equation then becomes a generalized matrix pseudo-eigenvalue problem. Solutions are obtained for the hydrogen molecule ion and H2 with a minimal AO basis. The Slater rule for 1s shells is rationalized via the optimal exponent in a minimal 1s basis. The nature of the chemical bond, and specifically the role of the kinetic energy in covalent bonding, are discussed in details with the example of the hydrogen molecule ion.

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Natural orbital functional calculations of molecular polarizabilities and second hyperpolarizabilities. The hydrogen molecule as a test case

Journal of Physics B Atomic Molecular and Optical Physics ◽

10.1088/0953-4075/47/1/015101 ◽

2013 ◽

Vol 47 (1) ◽

pp. 015101 ◽

Cited By ~ 6

Author(s):

Xabier Lopez ◽

Mario Piris ◽

Masayoshi Nakano ◽

Benoît Champagne

Keyword(s):

Hydrogen Molecule ◽

Test Case ◽

Natural Orbital ◽

Molecular Polarizabilities

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Coordination nano-space as stage of hydrogen ortho–para conversion

Royal Society Open Science ◽

10.1098/rsos.150006 ◽

2015 ◽

Vol 2 (7) ◽

pp. 150006 ◽

Cited By ~ 17

Author(s):

Takashi Kosone ◽

Akihiro Hori ◽

Eiji Nishibori ◽

Yoshiki Kubota ◽

Akio Mishima ◽

...

Keyword(s):

Electric Field ◽

Hydrogen Molecule ◽

X Ray Diffraction ◽

Porous Coordination Polymers ◽

X Ray ◽

Catalytic Hydrogen ◽

Spin Isomers ◽

And Control ◽

Physical And Chemical ◽

Density Study

The ability to design and control properties of nano-sized space in porous coordination polymers (PCPs) would provide us with an ideal stage for fascinating physical and chemical phenomena. We found an interconversion of nuclear-spin isomers for hydrogen molecule H 2 adsorbed in a Hofmann-type PCP, {Fe(pz)[Pd(CN) 4 ]} (pz=pyrazine), by the temperature dependence of Raman spectra. The ortho (o)–para (p) conversion process of H 2 is forbidden for an isolated molecule. The charge density study using synchrotron radiation X-ray diffraction reveals the electric field generated in coordination nano-space. The present results corroborate similar findings observed on different systems and confirm that o–p conversion can occur on non-magnetic solids and that electric field can induce the catalytic hydrogen o–p conversion.

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Compact representation of generalized molecular polarizabilities and efficient calculation of polarization energy in an arbitrary electric field

10.22541/au.162194953.36562067/v1 ◽

2021 ◽

Author(s):

Krzysztof Wolinski ◽

Peter Pulay

Keyword(s):

Electric Field ◽

Compact Representation ◽

Efficient Calculation ◽

Density Response Function ◽

Molecular Charge ◽

Order Of Magnitude ◽

Speed Up ◽

Molecular Polarizabilities ◽

Polarizability Matrix ◽

Natural Polarization

Generalized polarizabilities and the molecular charge distribution can describe the response of a molecule in an arbitrary static electric field up to second order. Depending on the expansion functions used to describe the perturbing potential, the generalized polarizability matrix can have rather large dimension (~1000). This matrix is the discretized version of the density response function or electronic susceptibility. Diagonalizing and truncating it can lead to significant (over an order of magnitude) speed-up in simulations. We have analyzed the convergence behavior of the generalized polarizability using a plane wave basis for the potential. The eigenfunctions of the generalized polarizability matrix are the natural polarization potentials. They are potentially useful to construct efficient polarizability models for molecules.

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Many-body calculation of the electric field gradient in the hydrogen molecule

International Journal of Quantum Chemistry ◽

10.1002/qua.560180617 ◽

1980 ◽

Vol 18 (6) ◽

pp. 1505-1510

Author(s):

T. Itagaki ◽

A. Saika

Keyword(s):

Electric Field ◽

Electric Field Gradient ◽

Field Gradient ◽

Hydrogen Molecule ◽

Many Body

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Chemical bond and entanglement of electrons in the hydrogen molecule

International Journal of Quantum Information ◽

10.1142/s0219749914500282 ◽

2014 ◽

Vol 12 (05) ◽

pp. 1450028

Author(s):

Nikos Iliopoulos ◽

Andreas F. Terzis

Keyword(s):

Linear Combination ◽

Chemical Bond ◽

Configuration Interaction ◽

Ground State ◽

Hydrogen Molecule ◽

Molecular System ◽

Quantum Correlations ◽

Atomic Orbitals ◽

Analytic Expression ◽

Electronic Wavefunction

We theoretically investigate the quantum correlations (in terms of concurrence of indistinguishable electrons) in a prototype molecular system (hydrogen molecule). With the assistance of the standard approximations of the linear combination of atomic orbitals and the configuration interaction methods we describe the electronic wavefunction of the ground state of the H 2 molecule. Moreover, we managed to find a rather simple analytic expression for the concurrence (the most used measure of quantum entanglement) of the two electrons when the molecule is in its lowest energy. We have found that concurrence does not really show any relation to the construction of the chemical bond.

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