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# Topic: Hartree-Fock

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 Hartree-Fock - Wikipedia, the free encyclopedia Fock, who improved the rigour of Hartree's method to make it consistent with the Pauli principle and reformulated it into the matrix form used today. A clever dodge, employed by Hartree, for atomic calculations was to increase the nuclear charge, thus pulling all the electrons closer together. The newly constructed Fock operator is then used as the Hamiltonian in the time-independent SchrÃ¶dinger Equation. en.wikipedia.org /wiki/Hartree-Fock   (1297 words)

 4.3.1 -Hartree-Fock Theory In general the calculation of each element of the Fock matrix requires access to all the elements of the density matrix and the array which holds the elements i,j,k,l (the Z matrix). After each send, the processor forms all the interactions that connect the current density and Fock matrix elements and then passes the data to the left and receives the new data from the right where the process is repeated. The density and Fock matrices are replicated onto each processor, each processor computes a subset of the integrals to form a partial Fock matrix. www.epcc.ed.ac.uk /overview/publications/training_material/tech_watch/98_tw/tw-molmod/molmod-21.html   (1497 words)

 10. Hartree-Fock or Self-consistent Field The underlying assumption in the use of symmetry in Fock matrix construction is that the density is totally symmetric. In a startup calculation (see Section 5.1), the default source for guess vectors is a diagonalized Fock matrix constructed from a superposition of the atomic density matrices for the particular problem. This directive enables/disables the use of symmetry to speed up Fock matrix construction (via the petite-list or skeleton algorithm) in the SCF, if symmetry was used in the specification of the geometry. www.emsl.pnl.gov /docs/nwchem/doc/user/node12.html   (5661 words)

 Hartree-Fock - Wikipedia, the free encyclopedia The Hartree-Fock method is typically used to solve the time-independent SchrÃ¶dinger equation for a multi-electron atom or molecule described in the fixed-nuclei approximation by the electronic molecular Hamiltonian. Fock, who demonstrated the rigour of Hartree's method and reformulated it into the matrix form used today. Under this approximation, (outlined under Hartree-Fock algorithm), all of the terms of the exact Hamiltonian except the nuclear-nuclear repulsion term are re-expressed as the sum of one-electron Fock operators. en.wikipedia.org /wiki/Hartree-Fock   (5661 words)

 Electronic problem: Hartree-Fock This dependence (exemplified in equations 1.25 and 1.26) forces that the Hartree-Fock equations must be solved iteratively until self-consistency. Equation 1.29 is a pseudo-eigenvalue equation because the Fock operator cannot be known unless we know the molecular orbitals, and molecular orbitals are obtained by the Fock operator. Its elements will be the coefficients to optimize in order to have a diagonal representation of the Fock matrix and therefore the pursued coefficients to obtain the molecular orbitals. klingon.uab.es /prat/Thesis/node10.html   (1328 words)

 Brian Hoffman's Publications Given the spatial form of the closed-shell Fock operator, the Hartree-Fock equation may be recast, as follows, in terms of spatial orbitals: and is the matrix representation of the Fock operator in the generic basis set. From the mathematics of linear algebra, this eigenvalue equation may be solved by diagonalizing the transformed Fock matrix zopyros.ccqc.uga.edu /~hoffbc/Source/scf/node10.html   (682 words)

 Hartree-Fock - (3) HF Equations The single-electron Hartree hamiltonian and the Coulomb component of the Hartree-Fock potential are both local operators. where h is the simplified Hartree hamiltonian for non-interacting electrons that we started with and the bracketed potential term is the extra Hartree-Fock potential arising from including electron-electron interactions with an antisymmetrized wave function. It is a Hartree-Fock correction term providing a lowering of the overall energy of interaction due to spin correlation keeping like-spin electrons being apart. hermes.phys.uwm.edu /projects/elecstruct/hermsk/HF/HF.Theory3.html   (503 words)

 Hartree Fock Equations As an initial guess for the fock matrix, one generally uses the core hamiltonian, ignoring all the two electron integrals. Without further ado, we'll introduce the spatial orbital based Fock operator and be done with it. Identifying the integrals as matrix elements of the fock operator and the unit operator (overlap) respectively, zopyros.ccqc.uga.edu /lec_top/hf/node6.html   (1181 words)

 Hartree-Fock Method are used to calculate the Coulomb and exchange operators and finally the Fock operator (eq 13). 's are used to construct a new Fock operator (eq 13) which is used to compute new F The new elements are substituted into the determinantal equation (eq 16), and it is solved to obtain a new set of values for the www.chm.davidson.edu /ronutt/che401/HartreeFock/HartreeFock.htm   (770 words)

 Supercomputer Institute Vol. 13 No. 1 Electron Problem article Conventional implementations of Hartree-Fock theory are dominated by computation of exchange and Coulomb contributions to the Fock matrix. Calculation of the two-electron integrals (and therefore the Fock matrix) is formally an N^4 process, where N is the number of basis functions. Linear scaling computation of the Fock matrix is achieved with specialized methods that exploit the unique characteristics of the exchange and Coulomb interactions. www.msi.umn.edu /general/Bulletin/Vol.13-No.1/ElectronProblem.html   (1032 words)

 The Hartree Fock Approximation Assessment Another name for the Hartree Fock Approximation is __________. www.shodor.org /chemviz/overview/hfaassess.html   (259 words)

 Douglas Hartree - Wikipedia, the free encyclopedia Hartree's last Ph.D. student at Cambridge, Charlotte Froese Fischer, would become world-famous for the development and implementation of the multi-configuration Hartree-Fock (MCHF) approach to atomic structure calculations and for her theoretical prediction concerning the existence of the negative calcium ion. Hartree moved to theoretical physics in 1937 before returning to Cambridge to take up the post of Plummer professor of mathematical physics in 1946. Douglas Rayner Hartree (March 27, 1897 - February 12, 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to atomic physics. en.wikipedia.org /wiki/Douglas_Hartree   (259 words)

 Hartree-Fock and Density Functional Theory To derive the Hartree Fock equations for a H The charge density, n, is then uniform and the Hartree term cancels the electron-ion term leaving only the kinetic energy and exchange terms only. This is, using atomic units and remembering the denominator is unity as the orbitals are orthonormal (including spin functions), newton.ex.ac.uk /teaching/resources/rj/theor_option/node5.html   (914 words)

 Hartree-Fock Theory If this contribution is ignored, then it is called the Hartree approximation. www.fyslab.hut.fi /~asf/physics/thesis1/node27.html   (219 words)

 The Hartree-Fock method It is seen that the first term in (1.10), which is called the Hartree energy, is equivalent to the classical Coulomb interaction between two charge densities. The HF-exchange energy is a non-positive function that has the important property that in the two summations of (1.10) its terms with a=b cancels with equivalent terms of the Hartree energy. In this report, when referring to the exchange energy, it will be the Kohn-Sham exchange energy, if not otherwise stated. dcwww.camp.dtu.dk /~bligaard/wwwdirectory/masterthesis/masterdirectory/project/node7.html   (931 words)

 Method of standard-less phase analysis by means of a diffractogram - US Patent 6108401 According to this Hartree-Fock method the volume of each of the atoms i, as required subsequently, is also obtained. The invention relates to a method of determining the concentrations of the constituents in a mixture of substances, in which for each of the substances the set of associated diffraction reflections is identified in a radiation diffractogram of the mixture and the relative intensities of each set of diffraction reflections are determined. This method implies that the integral in the left-hand term is determined from the known charge density distributions of the constituent electron clouds in the crystallographic unity cell. www.patentstorm.us /patents/6108401.html   (931 words)

 The Hartree-Fock Method It turns out that this needs to be done in an iterative way, because to solve what are called the Fock equations (which give the coefficients of the moleculars orbitals), one already needs to know the form of all the occupied orbitals (basically because one needs to be able to calculate J Solve the Fock equations, to give an improved set of orbitals. The atomic unit of energy is also called a Hartree and is equal to 4.35 10 www.chm.bris.ac.uk /pt/harvey/elstruct/hf_method.html   (1587 words)

 lcao_scf.word Fock operator (and the rest of the matrices) block into two parts, one for The disadvantage of this approach is that no restrictions are applied to retain symmetry properties of the wave function. Since the terms in the Hamiltonian operator have no spin dependence, there can be no terms in the energy involving orbitals of different spin (e.g., no hii). www.sdsc.edu /Education/Elemnet/structure/computations/compmenu/lcao_scf.html   (768 words)

 *HF INPUT It is our experience that it is usually most efficient not to perform any Roothaan Fock iterations before DIIS is activated, therefore, MAXFCK = 0 as default. Maximum number of closed-shell Roothaan  Fock iterations (default = 0). MAXFCK Roothaan Fock iterations (early exit if convergence or oscillations). www.lle.rochester.edu /pub/support/dalton/node113.html   (921 words)

 Hartree-Fock Self-Consistent Field Method The Hartree-Fock Self-Consistent Field Method is similar to the Hartree SCF Method, but takes the antisymmetry property into account by writing the trial wave function as a Slater determinant of variational spin-orbitals, Improvement over the one-determinant trial wave function can be achieved by using a trial wave function that involves a linear combination of Slater determinants. xbeams.chem.yale.edu /~batista/vvv/node30.html   (76 words)

 Overview of Computational Chemistry The original Hartree method expresses the total wavefunction of the system as a product of one-electron orbitals. www.shodor.org /chemviz/overview/hfa.html   (386 words)

 Hartree-Fock-Roothan Equations Spin Unrestricted Hartree Fock, and many others.) For all of these calculations, the equations are nearly the same. The easiest is the Restricted Hartree Fock (RHF) where only closed shells are considered. Open shell calculations are called Unrestricted Hartree Fock (UHF) or any of its variants (e.g. www.osc.edu /PET/CCM/skeleton/training/courses/foundations/qmnotes/node3.html   (1204 words)

 Michael Rust The simplest tactic is a kind of average field approximation originally due to Hartree and Fock. In the Hartree-Fock scheme we iteratively obtain approximate eigenvectors that are the "best" possible wavefunctions formed by products of single-electron wavefunctions. Unfortunately, no one has been able to figure out how to solve the more complicated eigenvalue problems resulting from molecules with more than a single electron. www.math.hmc.edu /seniorthesis/archives/2001/mrust/mrust-2001-prop.html   (817 words)

 Lecture 4: Uniform electron gas and simple metals It illustrates many aspects of the Hartree and Hartree-Fock approximations, where the properties can be calculated analytically. The homogeneous electron gas is the simplest model that captures the essence of the quantum state of electrons in condensed matter. Electron correlation can be treated by numerical methods and the resulting correlation functions illustrate salient features of the many-electron problem. www.physics.uiuc.edu /research/ElectronicStructure/598SCM-F04/lecture_outlines/lect04.html   (272 words)

 Chemistry - Wikipedia, the free encyclopedia In practice, only the simplest chemical systems may realistically be investigated in purely quantum mechanical terms, and approximations must be made for most practical purposes (e.g., Hartree-Fock, post Hartree-Fock or Density functional theory, see computational chemistry for more details). Hence a detailed understanding of quantum mechanics is not necessary for most chemistry, as the important implications of the theory (principally the orbital approximation) can be understood and applied in simpler terms. It is, in principle, possible to describe all chemical systems using this theory. en.wikipedia.org /wiki/Chemistry   (2334 words)

 teormet.doc Hartree-Fock method The essential idea of the Hartree-Fock or molecular orbital method is that, for a closed shell system, the electrons are assigned two at a time to a set of molecular orbitals. The molecular orbital method is generally referred to as the Hartree-Fock method. This is the sub class that uses the molecular orbital method, possibly followed by a post molecular orbital method that uses the molecular orbital wave function as the reference function. info.pue.udlap.mx /~mendezm/qcomp/teormet.doc   (2334 words)

 The Hartree-Fock method The major problem with the Hartee-Fock method, is that all the electron-electron interactions are approximated with the mean-field interaction. Thus, the many-electron wave function can be reduced to a product of several one-electron wave functions, a so called Hartree product. Therefore, the numerical self consistent field method (SCF) is used. www-rcf.usc.edu /~molsson/PhD/Thesis/node5.html   (2334 words)

 Ab initio method for finite lattice clusters The computational method used is based on a frozen core approximation, where the wavefunction is divided into valence and core orbitals [Pakkanen78,Whitten80]. The present method of classification applies to any system with translational symmetry, since it is not restricted to a basis function or an atom. The method is also not restricted to three dimensions, and in fact there are several cases where considerations of higher dimensions can be useful. www.chem.joensuu.fi /people/juha_muilu/Research/ab_initio_method.html   (2334 words)

 2.2 Atomic Solutions Instead, it is necessary, as it was in the non-relativistic theory, to appeal to approximate models such as the Dirac-Hartree-Fock (DHF) method. The resultant Fock operators[6] may be derived by requiring that the form of the occupied single particle spinors are variationally optimized with respect to the electronic energy. In the case that the atomic DHF wavefunction is to be represented on a numerical grid, some relatively straightforward boundary conditions may be applied in the occupation selection procedure to be sure that the final wavefunction is not contaminated by positronic solutions. zopyros.ccqc.uga.edu /lec_top/rltvt/node9.html   (2334 words)

 The Hartree-Fock Method - II The molecular orbitals are found from solving the Fock equation. Here are some examples to illustrate the level of accuracy (energies are in kJ/mol): www.chm.bris.ac.uk /pt/harvey/elstruct/hf_2.html   (1622 words)

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