Tetrel bonding interaction: an analysis with the block-localized wavefunction (BLW) approach

2019 ◽  
Vol 21 (22) ◽  
pp. 11776-11784 ◽  
Author(s):  
Changwei Wang ◽  
Yama Aman ◽  
Xiaoxi Ji ◽  
Yirong Mo
Keyword(s):  
Wave Function ◽  
Charge Transfer ◽  
The Self ◽  
Bonding Interaction ◽  
Self Consistent

In this study, fifty-one iconic tetrel bonding complexes were studied using the block localized wave function (BLW) method which can derive the self-consistent wavefunction for an electron-localized (diabatic) state where charge transfer is strictly deactivated.

scholarly journals A new model on DNA structure and thermal denaturation

2018 ◽  
Author(s):  
LUO Liaofu ◽  
YANG Guochen
Keyword(s):  
Wave Function ◽  
Thermal Denaturation ◽  
Collective Motion ◽  
Dna Structure ◽  
Simple Relation ◽  
The Self ◽  
Harmonic Potential ◽  
Large Temperature ◽  
Quantum Model ◽  
Self Consistent

AbstractA quantum model on DNA structure is proposed. By introducing the self-consistent harmonic potential in the X-Y plane vertical to helix axis (z-direction) and the periodic potential along the z-axis we obtain the wave function for the single nucleotide and the many-nucleotide system. The helix distribution of bases is deduced from the solution of wave function under the self-consistent potential. The variation of DNA structure (polymorphism) is related to the periodicity of the potential in Z-axis, the quantum state occurring in harmonic potential and the interaction between helix strands. As Watson-Crick (W-C) interaction is introduced between double helices, the quasi-particle transformation is utilized to solve the interacting many-body problem for DNA. It is proved that the phase-transition (thermal denaturation) temperature is related to the frequency ω of harmonic potential. Through comparison with experimental data a simple relation (N means number of base pairs and V the W-C coupling) is deduced. For a DNA sequence of 1000 bp ω is predicted about (0.9-1.2)×1017/sec. Such a high frequency is necessary for nucleotides of each strand located on a narrow tube. The large temperature fluctuation experimentally observed during DNA thermal denaturation is interpreted by the collective motion of nucleotides.

scholarly journals A generalization of the equations of the self-consistent field for two-electron configurations

1937 ◽  
Vol 160 (903) ◽  
pp. 588-604 ◽  
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Configuration Interaction ◽  
The Self ◽  
Angular Function ◽  
Radial Functions ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
General Method

The most successful general method so far devised for dealing with many- electron atoms is th a t of the self-consistent field (abbreviated in what follows to “ s. c. f.” ). If greater accuracy is required than is obtainable with the method as ordinarily used (either with or without exchange), either the so-called “ configuration interaction ” must be taken into account —usually a very laborious procedure—or else more complicated (varia­tional) methods must be used, which must be designed separately for each particular case, and in which the concept of each electron being assigned to its own “ orbit” is usually abandoned. It would seem desirable, therefore, to have, if possible, some general method which will increase the accuracy of the calculations without taking into account configuration interaction, and which will still allow the conceptual features of the s. c. f. method (i. e. the assignment of “ orbits” ) to be retained. In this paper such a method is developed for the case of two-electron configurations in Russell-Saunders coupling. The method consists in assuming a form for the wave function which is similar to that used in the s. c. f. method, except that the proper spatial symmetry is allowed for (which is not so in the case of the s. c. f. equations without exchange), and further, an adjustable function of Θ, the angle between the radii vectores to the two electrons, is inserted as a multiplying factor. The usual varia­tional method is then applied, and yields differential equations for the two radial functions which are similar to those of the ordinary theory, together with an equation for the angular function.

scholarly journals Self-consistent field with exchange for potassium and argon

1938 ◽  
Vol 166 (927) ◽  
pp. 450-464 ◽  
Keyword(s):  
Wave Function ◽  
Sufficient Accuracy ◽  
Wave Functions ◽  
The Self ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
The Difference

As already mentioned in a previous paper on the calculation of the self- consistent field with exchange for calcium (D. R. and W. Hartree 1938), wave functions more accurate than those calculated without exchange are required both for K + and for Ar, and the calculations for calcium were carried out partly in the hope that it would be possible to interpolate with sufficient accuracy the difference between the wave functions calculated with and without exchange for K + and Ar from the corresponding differences for Cl - and Ca ++ . The results showed that for the (I s ), (2 s ) and (2 p ) wave function this interpolation would probably be satisfactory, but for the (3 s ) and (3 p ) wave functions it was not as straightforward as had been hoped, though even for the latter wave functions, estimates of the differences could be made which, while rather uncertain, would probably give appreciably better wave functions than those calculated without exchange and taken without modification.

Note on the Interpretation of the Density Matrix in the Many-Electron Problem

1931 ◽  
Vol 27 (2) ◽  
pp. 240-243 ◽  
Author(s):  
P. A. M. Dirac
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Density Matrix ◽  
The Self ◽  
Transformation Theory ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
The Many

When we treat an atom containing a number n of electrons by the method of the self-consistent field, we assume that each electron has its own particular “orbit,” specified by a wave function (q|r) in four variables q. These four variables are usually taken to be the three coordinates of the electron together with a variable describing the spin, but according to the transformation theory of quantum mechanics, they may be any four independent commuting functions of the coordinates, momenta and spin variables.

scholarly journals The relativistic self-consistent field

1935 ◽  
Vol 152 (877) ◽  
pp. 625-649 ◽  
Keyword(s):  
Wave Equation ◽  
Field Equation ◽  
Wave Functions ◽  
The Self ◽  
Magnetic Interactions ◽  
Consistent Field ◽  
Exchange Effects ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Schrödinger's Equation

1—The method of the self-consistent field for determining the wave functions and energy levels of an atom with many electrons was developed by Hartree, and later derived from a variation principle and modified to take account of exchange and of Pauli’s exclusion principle by Slater* and Fock. No attempt was made to consider relativity effects, and the use of “ spin ” wave functions was purely formal. Since, in the solution of Dirac’s equation for a hydrogen-like atom of nuclear charge Z, the difference of the radial wave functions from the solutions of Schrodinger’s equation depends on the ratio Z/137, it appears that for heavy atoms the relativity correction will be of importance; in fact, it may in some cases be of more importance as a modification of Hartree’s original self-nsistent field equation than “ exchange ” effects. The relativistic self-consistent field equation neglecting “ exchange ” terms can be formed from Dirac’s equation by a method completely analogous to Hartree’s original derivation of the non-relativistic self-consistent field equation from Schrodinger’s equation. Here we are concerned with including both relativity and “ exchange ” effects and we show how Slater’s varia-tional method may be extended for this purpose. A difficulty arises in considering the relativistic theory of any problem concerning more than one electron since the correct wave equation for such a system is not known. Formulae have been given for the inter-action energy of two electrons, taking account of magnetic interactions and retardation, by Gaunt, Breit, and others. Since, however, none of these is to be regarded as exact, in the present paper the crude electrostatic expression for the potential energy will be used. The neglect of the magnetic interactions is not likely to lead to any great error for an atom consisting mainly of closed groups, since the magnetic field of a closed group vanishes. Also, since the self-consistent field type of approximation is concerned with the interaction of average distributions of electrons in one-electron wave functions, it seems probable that retardation does not play an important part. These effects are in any case likely to be of less importance than the improvement in the grouping of the wave functions which arises from using a wave equation which involves the spins implicitly.

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