Hartree, Douglas

All the early work was concerned with atoms, with Sir William Hartree regarded as the father of the technique. His son, Douglas R. Hartree, published the definitive book, The Calculation of Atomic Structures, in 1957, and in this he derived the atomic HF equations and described numerical algorithms for their solution. Charlotte Froese Fischer was a research student working under the guidance of D. R. Hartree, and she published her own definitive book. The Hartree—Fock Method for Atoms A Numerical Approach in 1977. The Appendix lists a number of freely available atomie structure programs. Most of these can be obtained from the Computer Physics Communications Program Library. 

Sir William Hartree developed ingenious ways of solving the radial equation, and they are documented in Douglas R. Hartree s book (1957). By the time this book was published, the SCF method had been well developed, and its connection with the variation principle was finally understood. It is interesting to note that Chapter 2 of Douglas R. Hartree s book deals with the variation principle. 

Douglas, A. S., Proc. Cambridge Phil. Soc. 52, 687, "A method for improving energy-level calculations for series electrons." Inclusion of a polarization potential in the Hartree-Slater-Fock equation. 

If not otherwise stated the four-component Dirac method was used. The Hartree-Fock (HF) calculations are numerical and contain Breit and QED corrections (self-energy and vacuum polarization). For Au and Rg, the Fock-space coupled cluster (CC) results are taken from Kaldor and co-workers [4, 90], which contains the Breit term in the low-frequency limit. For Cu and Ag, Douglas-Kroll scalar relativistic CCSD(T) results are used from Sadlej and co-workers [6]. Experimental values are from Refs. [91, 92]. 

Pempointner, M., Seth, M. and Schwerdtfeger, P. (1998) A Point-Charge Model for the Nuclear Quadmpole Moment. Accurate Coupled-Cluster, Dirac-Fock, Douglas-KroD and Nomelativistic Hartree-Fock Calculations... 

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... 

For a discussion of the self-consistent field, see Schweber (1990 375376). Hartree became professor of theoretical physics at Manchester and returned to Cambridge University after the war. For his own account of his method, see Douglas Hartree, The Calculations of Atomic Structures (New York Wiley, 1957). 

Douglas Hartree, bom Cambridge, England, 1897. Ph.D. Cambridge, 1926. Professor applied mathematics, theoretical physics, Manchester, Cambridge. Died Cambridge, 1958. 

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

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 ... 

Accounting for relativistic effects in computational organotin studies becomes complicated, because Hartree-Fock (HF), density functional theory (DFT), and post-HF methods such as n-th order Mpller-Plesset perturbation (MPn), coupled cluster (CC), and quadratic configuration interaction (QCI) methods are non-relativistic. Relativistic effects can be incorporated in quantum chemical methods with Dirac-Hartree-Fock theory, which is based on the four-component Dirac equation. " Unformnately the four-component Flamiltonian in the all-electron relativistic Dirac-Fock method makes calculations time consuming, with calculations becoming 100 times more expensive. The four-component Dirac equation can be approximated by a two-component form, as seen in the Douglas-Kroll (DK) Hamiltonian or by the zero-order regular approximation To address the electron cor-... 

In the 1930s Douglas Hartree and his father William Hartree used a mechanical analog computer to explore the idea that an electron in an atom moves partly in the attractive potential of the nucleus and partly in an averaged repulsive potential due to all the other electrons. Later, V. Fock added to the Hartrees model an exchange term due to the effects of the antisymmetry of the many-electron wave function. The Hartree-Fock approximation is still a basic tool of quantum chemistry. 

Bond lengths R (A), binding energies D. (eV) and vibrational constants a>e (cm ) of the homonuclear halogen dimers from dl-electron (AE) Douglas-Kroll-HeB (DKH) and valence-only energy-consistent pseudopotential (EC-PP) Hartree-Fock self-consistent field (SCF) calculations. The effects of static and dynamic core-polarization at the valence-only level are modelled by a core-polarization potential (CPP). 

C. Eroese Eischer, Douglas Rayner Hartree His life in science and computing. World Scientific Publishing, New Jersey, 2003. 

Equilibrium distances r, vibrational constants (Og and dissociation energies Dg for the ground state of molecular iodine, fium Ref. [102], All-electron (AE) calculations are obtained from either the scalar-relativistic Douglas-Kroll-HeB (DKH) approximation or 4-component Dirac-Hartree-Fock (DHF) correlated calculation taken from Ref [103]. 

Professor Douglas R. Hartree, Numerical Analysis [1952 The Clarendon Press, Oxford, England]... 

Douglas R. Hartree (1897-1958) was born and died in Cambridge, U.K. He was a British mathematician and physicist, professor at Manchester University, and then professor of mathematical physics at Cambridge. Until 1921, his interest was in the development of numerical methods for anti-aircraft artillery (he had some experience from World War I), but a lecture by Niels Bohr has completely changed his career. Hartree immediately started investigating atoms. He used the atomic wave function in the form of the spinorbital product. Hartree learned to use machines to solve differential... 

The exchange operator represents a (non-intuitive) result of the antisymmetrization postulate for the total wave function (Chapter 1) and it has no classical interpretation. If the variational wave function were the product of the spinorbitals (Douglas Hartree did this in the beginning of quantum chemistiy),... 

It is remarkable that as early as 1927, Douglas Hartree pioneered a self-consistent fleld method (SCF) for theory of atoms. Hartree proposed the numerical iterative technique for solution to quantum equations. 

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]. 

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