Comparison of diborane molecular properties from minimum basis set and extended Slater orbital wave functions

1972 ◽  
Vol 94 (13) ◽  
pp. 4461-4467 ◽  
Author(s):  
Edward A. Laws ◽  
Richard M. Stevens ◽  
William N. Lipscomb
Keyword(s):  
Wave Functions ◽  
Molecular Properties ◽  
Basis Set ◽  
Slater Orbital

scholarly journals Towards the Search for Thallium Nuclear Schiff Moment in Polyatomic Molecules: Molecular Properties of Thallium Monocyanide (TlCN)

Atoms ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 62 ◽  
Author(s):  
A. Kudrin ◽  
A. Zaitsevskii ◽  
T. Isaev ◽  
D. Maison ◽  
L. Skripnikov
Keyword(s):  
Inner Core ◽  
Molecular Properties ◽  
Basis Set ◽  
Cluster Method ◽  
Coupled Cluster ◽  
The Core ◽  
Complete Basis Set ◽  
Core Electrons ◽  
Complete Basis Set Limit ◽  
Potential Energy Minimum

Molecular properties of the thallium monocyanide (Tl·CN) system in its ground electronic state are studied using high-precision ab initio relativistic two-component pseudopotential replacing 60 inner-core electrons of Tl. A relativistic coupled-cluster method with single, double and perturbative triple amplitudes is employed to account for electronic correlations. Extrapolation of results to the complete basis set limit is used for all studied properties. The global potential energy minimum of Tl·CN corresponds to the linear cyanide (TlCN) isomer, while the non-rigid isocyanide-like (TlNC) structure lies by approximately 11 kJ/mol higher in energy. The procedure of restoration of the wavefunction in the “core” region of Tl atom was applied to calculate the interaction of the Tl nuclear Schiff moment with electrons. The parameter X of the interaction of the Tl nuclear Schiff moment with electrons in the linear TlCN molecule equals 7150 a.u. The prospects of using the TlCN molecule for the experimental detection of the nuclear Schiff moment are discussed.

Basis-Set Expansions of Relativistic Electronic Wave Functions

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Relativistic Quantum ◽  
Finite Basis ◽  
Wave Functions ◽  
Basis Set ◽  
Electronic Wave ◽  
Nonrelativistic Case ◽  
Hartree Fock ◽  
Electronic Wave Functions ◽  
Basis Set Expansion ◽  
Molecular Calculations

There have been several successful applications of the Dirac–Hartree–Fock (DHF) equations to the calculation of numerical electronic wave functions for diatomic molecules (Laaksonen and Grant 1984a, 1984b, Sundholm 1988, 1994, Kullie et al. 1999). However, the use of numerical techniques in relativistic molecular calculations encounters the same difficulties as in the nonrelativistic case, and to proceed to general applications beyond simple diatomic and linear molecules it is necessary to resort to an analytic approximation using a basis set expansion of the wave function. The techniques for such calculations may to a large extent be based on the methods developed for nonrelativistic calculations, but it turns out that the transfer of these methods to the relativistic case requires special considerations. These considerations, as well as the development of the finite basis versions of both the Dirac and DHF equations, form the subject of the present chapter. In particular, in the early days of relativistic quantum chemistry, attempts to solve the DHF equations in a basis set expansion sometimes led to unexpected results. One of the problems was that some calculations did not tend to the correct nonrelativistic limit. Subsequent investigations revealed that this was caused by inconsistencies in the choice of basis set for the small-component space, and some basic principles of basisset selection for relativistic calculations were established. The variational stability of the DHF equations in a finite basis has also been a subject of debate. As we show in this chapter, it is possible to establish lower variational bounds, thus ensuring that the iterative solution of the DHF equations does not collapse. There are two basically different strategies that may be followed when developing a finite basis formulation for relativistic molecular calculations. One possibility is to expand the large and small components of the 4-spinor in a basis of 2-spinors. The alternative is to expand each of the scalar components of the 4-spinor in a scalar basis. Both approaches have their advantages and disadvantages, though the latter approach is obviously the easier one for adapting nonrelativistic methods, which work in real scalar arithmetic.

Basis Set Superposition Errors in the Many-Body Expansion of Molecular Properties

2019 ◽  
Vol 123 (20) ◽  
pp. 4500-4511 ◽  
Author(s):  
Benjamin G. Peyton ◽  
T. Daniel Crawford
Keyword(s):  
Molecular Properties ◽  
Basis Set ◽  
Many Body ◽  
The Many

scholarly journals Discrete-basis-set method for electron-molecule continuum wave functions

1978 ◽  
Vol 18 (5) ◽  
pp. 2107-2114 ◽  
Author(s):  
Arne W. Fliflet ◽  
Vincent McKoy
Keyword(s):  
Wave Functions ◽  
Basis Set ◽  
Continuum Wave

Molecular orbitals in momentum space

1965 ◽  
Vol 286 (1406) ◽  
pp. 376-389 ◽  
Keyword(s):  
Momentum Space ◽  
Wave Functions ◽  
Basis Set ◽  
Equilibrium Distance ◽  
Numerical Work ◽  
Algebraic Expressions ◽  
Unitary Transformations ◽  
The Matrix ◽  
Internuclear Distances ◽  
Ground State Energies

The troublesome problem of developing cusps in ordinary molecular wave functions can be avoided by working with momentum-space wavefunctions for these have no cusps. The need for continuum wavefunctions can be eliminated if one works with a hydrogenic basis set in Fock’s projective momentmn space. This basis set is the set of R 4 spherical harmonics and as a consequence one may obtain, solely by the ordinary angular momentum calculus, algebraic expressions for all the integrals required in the solution of the momentum space Schrödinger equation. A number of these integrals and a number of R 4 transformation coefficients are tabulated. The method is then applied to several simple united-atom and l.c.a.o. wavefunctions for H + 2 and ground state energies and corrected wavefunctions are obtained. It is found in this numerical work that the method is most appropriate at internuclear distances somewhat less than the equilibrium distance. In Fock’s representation both l.c.a.o. and unitedatom approximations become exact as the internuclear distance approaches zero. The united-atom expansion can be viewed as an eigenvalue equation for the root-mean-square momentum, p 0 = √( — 2 E ). In the molecule, the matrix operator corresponding to p 0 is related to the operator for the united-atom by a sum of unitary transformations, one for each nucleus in the molecule.

Ab initio Calculations of the Rotation-Vibration Spectrum of Na3+

1993 ◽  
Vol 58 (1) ◽  
pp. 24-28 ◽  
Author(s):  
Ladislav Češpiva ◽  
Vlasta Bonačič-Koutecký ◽  
Jaroslav Koutecký ◽  
Per Jensen ◽  
Vojtěch Hrouda ◽  
...  
Keyword(s):  
Potential Surface ◽  
Vibration Spectrum ◽  
Wave Functions ◽  
Basis Set ◽  
Morse Oscillator ◽  
Fundamental Frequencies ◽  
Rotational Wave ◽  
Rigid Molecule ◽  
Full Ci ◽  
Ci Calculations

SCF, 6C-SCF, MP4 and valence-electron full CI calculations were performed in order to determine the potential surface of Na3+. A power series in the variables yi = 1 - exp (-a∆ri), where ∆ri are bond length displacements from equilibrium, has been fitted through the surface obtained and used in a variational rotation-vibration calculations with a basis set of products of Morse-oscillator eigenfunctions and symmetric top rotational wave functions. In contrast to H3+, Na3+ behaves as a very rigid molecule and does not exhibit any anomalous anharmonicity. With our best potential surface, MP4, the predicted E' and A1' fundamental frequencies are 105.1 and 146.7 cm-1, and the harmonic E' and A1' frequencies are 106.5 and 148.3 cm-1.

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