• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
Elliptic Preconditioner for Accelerating the Self
Elliptic Preconditioner for Accelerating the Self

... Fermi–Dirac function evaluated at εi . When β is sufficiently large, the Fermi–Dirac function behaves like a step function that drops from 1 to 0 at μ (which lies between εN and εN +1 ). Spin degeneracy is omitted here for simplicity. In this paper, we assume the Kohn–Sham system (1.1) is defined withi ...
The Polarizable Continuum Model Goes Viral! - Munin
The Polarizable Continuum Model Goes Viral! - Munin

... to the availability of efficient and accurate ab initio quantum chemical models. Limitations to such an approach do, however, still exist. The vast majority of chemical phenomena happens in complex environments, where the molecule of interest can interact with a large number of other moieties, solve ...
Duo: A general program for calculating spectra of diatomic molecules
Duo: A general program for calculating spectra of diatomic molecules

... rise to r-dependent curves; these can be computed by ab initio methods [61] or estimated semi-empirically, for example using quantum defect theory [62,63]. The expectation value of the sum of the vibrational and the mass-polarization Hamiltonian using the electronic wave functions gives rise [58,64] ...
Basis Sets in Quantum Chemistry C. David Sherrill School of
Basis Sets in Quantum Chemistry C. David Sherrill School of

... newer Pople basis sets like 6-311G(3df)], some using 6 d’s [older Pople basis sets like 6-31G(d)]; results don’t change much, but it is more consistent to use the same number of polarization functions as the basis set designer • Different programs have different default values for number of polariza ...
Inner-shell excitation of open-shell atoms - Shih
Inner-shell excitation of open-shell atoms - Shih

... to correlation energies of atomic systems with smaller Z, the LYP results are generally worse than the PW results for atomic systems with Z  8. For the total energies of excited states 1s2snp 2,4 P (n = 2–8) given in table 2, the maximum relative discrepancies of our PW and LYP results are 0.56% an ...
PDF Full-text
PDF Full-text

... valence atomic orbitals [3,4]. Molecular Orbital, MO, theory, an early alternative to VB theory, has a less obvious connection to molecular structural formulas and has been more usually associated with electronic spectroscopy. It was shown in 1935 by Van Vleck and Sherman that VB theory and MO theor ...
Implications of the two nodal domains conjecture for ground state
Implications of the two nodal domains conjecture for ground state

... forward related to the nodes of the fermionic ground state of a many-body system, namely that there is a single nodal hypersurface that divides configuration space into only two connected domains. While this is obviously relevant to the fixed node diffusion Monte Carlo method, its repercussions have r ...
A  comparative analysis  of two methods for the... of electric-field-induced  perturbations to molecular vibration
A comparative analysis of two methods for the... of electric-field-induced perturbations to molecular vibration

... There is growing interest in the effect of electric fields on molecular vibration and this complements the picture we already have of the effects of an electric field on electronic motion. The latter effects are conventionally described in terms of the dipole polarizability (a) and hyperpolarizabili ...
Thesis - Institut für Physik
Thesis - Institut für Physik

... 1.1. Structure of this Thesis This thesis is divided into seven chapters plus appendix. Especially the introductory chapters of this thesis follow the path of a handful of wonderful summaries of first theoretical predictions and descriptions as well as underlying experiments and historical backgroun ...
New efficient integral algorithms for quantum chemistry
New efficient integral algorithms for quantum chemistry

... within the following decade, extending to the entire molecule the orbital description, and using empirical data to estimate the value of the matrix elements. As computers became faster and memory increased, the number of atoms that could be treated with semiempirical methods also increased, and more ...
Quantum Monte Carlo simulations of solids W. M. C. Foulkes
Quantum Monte Carlo simulations of solids W. M. C. Foulkes

... positions, and Z ␣ are the nuclear charges.1 The first quantum-mechanical studies of chemically bonded systems appeared soon after the birth of quantum mechanics. Heitler and London (1927) calculated the binding energy and internuclear separation of H2 by approximating the wave function as an antisy ...
VARIATIONAL MONTE CARLO ESTIMATION OF THE
VARIATIONAL MONTE CARLO ESTIMATION OF THE

... In this work we would like to present a new approach to computation of dissociation energy De of CuH using the variational Monte Carlo (VMC) method. In Chapter 2 we give a historical overview of different ab. initio methods used in quantum chemistry nowadays. The emphasis is on quantum Monte Carlo ( ...
Chapter 1 exercises - Cognella Titles Store
Chapter 1 exercises - Cognella Titles Store

... in which the human family found itself. Of these, chemistry uniquely stood at the fateful intersection of careful observation and innovative application. On the one hand, it was realized by the earliest practitioners of the chemical sciences (the metallurgists who focused on the properties of ores a ...
Solvation of electronically excited I2-
Solvation of electronically excited I2-

... While the weak field Hamiltonian does capture the essence of the model, its extension to include arbitrary electrostatic interactions requires matrix elements of the electrostatic interaction with respect to the many-electron eigenfunctions of isolated Ii. These eigenfunctions have a relatively comp ...
The use of spin-pure and non-orthogonal Hilbert spaces in Full
The use of spin-pure and non-orthogonal Hilbert spaces in Full

... of a molecule fully, and theoreticians are required to make approximations which compromise accuracy for tractability. Indeed, as Dirac famously stated in 1929:1 The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus complete ...
Fluorinated Butatrienes - diss.fu-berlin.de
Fluorinated Butatrienes - diss.fu-berlin.de

... The present study provides deeper insight into the chemistry of fluorinated butatrienes both experimentally and theoretically. The four step synthesis of tetrafluorobutatriene starting from commercially available 1,1difluoroethylene could be successfully improved to an overall yield of up to 42% (fr ...
The atomic orbitals of the topological atom
The atomic orbitals of the topological atom

... In practice, the dimension of the “effective AO” basis has nothing to do with the dimension of the LCAO basis (if any) used in the original calculation. Equation (6) indicates that the maximum number of “effective AOs” that can be obtained is Nat × n, which can be both less or more than the total nu ...
Photodissociation Dynamics R. Schinke
Photodissociation Dynamics R. Schinke

... the shape of the potential near the FC region, where the molecule is still bound. 2. The Raman spectrum, i.e., the dispersed spectrum of light that the dissociating molecule emits to a lower-lying electronic state on its way from the FC region to the fragments, if.R/ , provides knowledge about a wi ...
Ground-state stability and criticality of two-electron atoms
Ground-state stability and criticality of two-electron atoms

... physics. The behavior of systems near a binding threshold is important in the study of ionization of atoms and molecules, molecule dissociation, and scattering collisions. Since the pioneering works of Bethe [1] and Hylleraas[2] confirming the existence of the negative hydrogen ion, H − , the study ...
Hybridization of atomic orbitals
Hybridization of atomic orbitals

... Atomic orbitals are (energy) states or wave forms of electrons in the atom. If we insist on the particle nature of electrons, then the probability of finding an electron in an atomic orbital is proportional to the square of the wavefunction. The values of the wavefunction can be either positive or n ...
A Bird`s-Eye View of Density-Functional Theory
A Bird`s-Eye View of Density-Functional Theory

... One sometimes says that T̂ and Û are ‘universal’, while V̂ is systemdependent, or ‘nonuniversal’. We will come back to this terminology. A simple estimate of the computational complexity of this task is to imagine a real-space representation of Ψ on a mesh, in which each coordinate is discretized b ...
A Bird`s-Eye View of Density
A Bird`s-Eye View of Density

... many-body problem, with Û, onto a single-body problem, without Û. All this is done by promoting the particle density n(r) from just one among many observables to the status of key variable, on which the calculation of all other observables can be based. This approach forms the basis of the large m ...
Electronic Structure of Clusters and Nanocrystals
Electronic Structure of Clusters and Nanocrystals

... A number of highly successful approximations have been made to solve for the both the ground state and excited state energies. For the most part, these approximations used are to remove as many “irrelevant” degrees of freedom from the system as possible. One common approximation is to separate the n ...
Measurement of the quantum capacitance of interacting electrons in
Measurement of the quantum capacitance of interacting electrons in

... leads pinched-off, Vbg = 0) gives the baseline stray capacitance, which is independent of Vtg . In contrast, with n- or p-type leads (Vbg = +7 V/ − 7 V red/blue curves respectively) the capacitance has a well-pronounced structure—a large dip in the centre followed by symmetric structures at its posit ...
Molecular Geometry and Hybridization
Molecular Geometry and Hybridization

... A covalent bond forms when orbitals of two atoms overlap. This overlap is occupied by a pair of electrons having high probability of being located between the nuclei of two atoms. Linus Pauling proposed that the valence atomic orbitals in a molecule are different from those in the isolated atoms. Th ...
< 1 2 3 4 5 6 7 ... 29 >

Hartree–Fock method

In computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state.The Hartree–Fock method often assumes that the exact, N-body wave function of the system can be approximated by a single Slater determinant (in the case where the particles are fermions) or by a single permanent (in the case of bosons) of N spin-orbitals. By invoking the variational method, one can derive a set of N-coupled equations for the N spin orbitals. A solution of these equations yields the Hartree–Fock wave function and energy of the system.Especially in the older literature, the Hartree–Fock method is also called the self-consistent field method (SCF). In deriving what is now called the Hartree equation as an approximate solution of the Schrödinger equation, Hartree required the final field as computed from the charge distribution to be ""self-consistent"" with the assumed initial field. Thus, self-consistency was a requirement of the solution. The solutions to the non-linear Hartree–Fock equations also behave as if each particle is subjected to the mean field created by all other particles (see the Fock operator below) and hence the terminology continued. The equations are almost universally solved by means of an iterative method, although the fixed-point iteration algorithm does not always converge.This solution scheme is not the only one possible and is not an essential feature of the Hartree–Fock method.The Hartree–Fock method finds its typical application in the solution of the Schrödinger equation for atoms, molecules, nanostructures and solids but it has also found widespread use in nuclear physics. (See Hartree–Fock–Bogoliubov method for a discussion of its application in nuclear structure theory). In atomic structure theory, calculations may be for a spectrum with many excited energy levels and consequently the Hartree–Fock method for atoms assumes the wave function is a single configuration state function with well-defined quantum numbers and that the energy level is not necessarily the ground state.For both atoms and molecules, the Hartree–Fock solution is the central starting point for most methods that describe the many-electron system more accurately.The rest of this article will focus on applications in electronic structure theory suitable for molecules with the atom as a special case.The discussion here is only for the Restricted Hartree–Fock method, where the atom or molecule is a closed-shell system with all orbitals (atomic or molecular) doubly occupied. Open-shell systems, where some of the electrons are not paired, can be dealt with by one of two Hartree–Fock methods: Restricted open-shell Hartree–Fock (ROHF) Unrestricted Hartree–Fock (UHF)↑ ↑
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report