Fock,Vladimir

About the same time, Douglas Hartree, along with other members of the informal club for theoretical physics at Cambridge University called the Del-Squared Club, began studying approximate methods to describe many-electron atoms. Hartree developed the method of the self-consistent field, which was improved by Vladimir Fock and Slater in early 1930, so as to incorporate the Pauli principle ab initio.37 Dirac, another Del-Squared member, published a paper in 1929 which focused on the exchange interaction of identical particles. This work became part of what soon became called the Heisenberg-Dirac approach.38... 

Douglas Rayner Hartree (1897-1958). Vladimir Aleksandrovich Fock (1898-1974). Clemens C. J. Roothaan (1918- ). 

The Russian mathematician Vladimir Aleksandrovich Fock (1898-1974) extended the Hartree equahon by considering this anhsymmetry (Fock, 1930), resulting in what is called the Fock, or Hartree-Fock, equahon (for a derivahon, see Thijssen, 1999). With the Hartree-Fock approximahon, the following term is added to Eq. 4.7 ... 

There is an obvious vicious circle in this approach if the spatial distribution of each electron is one of the unknowns, how can we speak of averaged distributions The answer is an iterative numerical calculation as demonstrated originally by the British physicist Douglas Hartree in 1928. In 1930, the method was improved by the Russian physicist Vladimir Fock who adapted the method to antisymmetric wavefunctions as required by the Pauli principle. The Hartree-Fock method is a numerical calculation that can be summarized in the following steps ... 

Douglat Hartree 0897 - 1958) and Vladimir Fock 0898 -1974) in the 1930s proposed a technique forthe approximate calculation of the wave function ofthe molecule. 

This equation was solved for the hydrogen atom by Vladimir Fock [2,3]. The solution in p space revealed the four-dimensional symmetry responsible for the degeneracy of states with the same n but different I quantum numbers in the hydrogen atom. This is a fine example where the momentum-space perspective led to fresh and deep insight. Fock s work spawned much further research on dynamical groups and spectrum-generating algebras. 

Vladimir A. Fock (1898-1974), Russian physicist, professor at Leningrad University (Saint Petersburg), led investigations on quantum mechanics, gravity theory, general relativity theory, and in 1930. while explaining atomic spectra, invented the antisymmetrizaHon of the spinorbitals product. 

Vladimir Fock developed a technique known as the Hartree-Fock theory, which takes into account the exchange energy of electrons. 

Fock degeneracy A hidden degeneracy that occurs in the spectrum of the hydrogen atom as a result of the rotational invariance in four dimensions associated with the Coulomb interation between the proton and the electron, ft was discovered by the Soviet physicist Vladimir Fock (1898-1974) in 1935. 

The semiempirical approach was meant to overcome the barriers represented by the difficulties in calculating integrals. For the more difficult ones approximations were introduced, while for others parameters were adjusted by empirically fitting the experimental data. In time, the semiempirical methods were superseded by more modem approaches, but they had had a pioneering contribution not only by providing a plethora of results, but also by educating the community of chemists to the possibilities of quantum chemical computations and wetted their appetites for more. The approximate methods of Vladimir A. Fock (Fig. 1.17a) and Douglas R. Hartree (Fig. 1.17b) [46] pointed the way toward the more objective non-empirical or ab initio techniques [47]. 

Fig. 1.17 (a) Vladimir A. Fock (Courtesy of the late Lev Vilkov) (b) Douglas R. Haitree (Fischer CF (2004) Douglas Rayner Hartree His life in science and computing. World Scientific, Singapore)... 

Later, J. C. Slater showed that the Hartree equations can be obtained if the variation principle is applied to a product of spin orbitals. The Russian theoretical physicist Vladimir A. Lock pointed out that certain symmetry conditions are not obeyed in the Hartree method, of which the most important one is the antisymmetric property of the total wave function. The variation principle was now applied to an antisymmetrized product of spin orbitals, that is, a Slater determinant. This is a fnndamen-tal method in electronic structure calculations and is referred to as the Hartree-Fock method or simply Hartree-Eock. ... 

One method for finding a numerical solution to a many-body problem is the Hartree-Fock method [3], devised in the late 1920s by Hartree [4] and refined by Vladimir Fock (though it wasn t until later that the equations were refined and implemented in computational code). Hartree-Fock methods are computationally very expensive, and inherent in the equations are a number of approximations that introduce artefacts in the computational model. These must be borne in mind when interpreting the results. Not least of them is the Bom-Oppenheimer approximation, which separates the nuclear and electronic wavefiinctions. ... 

The technique was applied to the atoms of He, Rb, Na, Cl . And it was the justification of Hartree s method that got Slater (1929) to think more about the theory of complex spectra, introducing determinants and the variational method for deriving analytically the self-consistent field equations with the right symmetry properties, as we have already discussed in chapter 2. Furthermore, Vladimir Fock (1930) also... 

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