C. Froese Fischer and D. Ellis
... The programs that generate expansions deal in terms
of subshells of configurations, without regard to coupling [13, 14]. For a given case, electrons are assigned
to subshells. Electrons are then replaced by electrons
from a list of allowed subshells according to some
rule, and then all possible conf ...
Perspective: Fifty years of density-functional theory in chemical physics
... densities from other sources, TFD energies have errors of
around 10%, too large for computational purposes. Furthermore, Teller deduced13 that Thomas-Fermi theory cannot bind
molecules. TFD is useful for rough estimates of atomic properties only.
Shell structure is a consequence of the Pauli exclusi ...
Establishing Quantum Monte Carlo and Hybrid Density Functional
... require a solution of the fundamental many-electron Schrödinger equation. Since an exact solution of Schrödinger’s equation is intractable, several numerical methods have been
developed to obtain approximate solutions. Currently, the two most successful methods
are density functional theory (DFT) ...
Ultracold Fermions in Two-Dimensional Planes with Dipolar
... in the rovibrational ground state. The strategy which lead to success was to first cool down atoms and
then coherently convert them to ground state molecules at low temperatures without heating the sample.
Mainly this is done by the use of Feshbach resonance to switch the interaction after the cooli ...
Chem Soc Rev - [ RSC ] Publishing
... a detailed study on the equilibrium between the peroxo and bis(m-oxo) isomers of [Cu2(en)2(O)2]2+. In this case, the scan of the
potential energy surface (PES) connecting the two structures was
conducted using LPNO-CCSD energies in the complete basis set
limit complemented with canonical perturbativ ...
Ab initio Calculations of Optical Rotation
... smells like speariment, while its right-handed counterpart smells like caraway. 1 (R)-limonene is
found in orange peels, while the (S ) enantiomer is present in lemons.2 Often, one enantiomer
produces a characteristic effect, while the other either produces no effect at all, or has a totally
Synthesizing arbitrary quantum states in a superconducting resonator
... photons in a completely controlled and deterministic manner. We
synthesize the states using a superconducting phase qubit to
phase-coherently pump photons into the resonator, making use
of an algorithm7 that generalizes a previously demonstrated
method of generating photon number (Fock) states in a
Chapter 5 | Molecular Orbitals
... Although apparently satisfactory Lewis electron-dot structures of N2, O2, and F2 can be
drawn, the same is not true with Li2, Be2, B2, and C2, which violate the octet rule. In addition, the Lewis structure of O2 predicts a double-bonded, diamagnetic (all electrons paired)
molecule ( O O ), but exper ...
Electronic-structure calculations by first-principles
... Wesolowski, Warshal, and Weber 22 to examine a solute in
solution and by Truong and co-workers to study the adsorption of water on NaCl~001!.23 Our method, discussed in subsequent sections, is related to these ideas.
In the early 80’s, Whitten et al.29 developed the first
cluster-in-cluster embeddin ...
Resolution-of-identity approach to Hartree–Fock, hybrid
... where Ne is the number of electrons that interact via the Coulomb interaction vieej ≡ 1/|ri − r j |,
and viext ≡ vext (ri ) is a local, multiplicative external potential, usually due to the nuclei. Hartree
atomic units are used throughout this paper. The numerical cost for an exact solution of the
Reconstruction on Wigner Functions on Different
... It is well known that the wave-function of a quantum-mechanical system cannot
be measured directly . A single measurement does not yield enough information which allows us to determine the state of the system uniquely . In addition, due to the fact that conjugated observables do not commute, ...
Excited states from time-dependent density functional theory
... This work focuses primarily on the linear response
regime. Throughout, we emphasize the difference between small molecules (atoms, diatomics, etc.) and the
larger molecules that are of greater practical interest,
where TDDFT is often the only practical first-principles
method. We use napthalene (C10 ...
... theory to explain the terminology used in later chapters.
The core of this book is the description of the many computation techniques
available and when to use them. Prioritizing which techniques work better or
worse for various types of problems is a double-edged sword. This is certainly
the type o ...
THEORETICAL AND COMPUTATIONAL METHODS
... More specifically, the thesis discusses the calculation of the H+H+H three-body recombination rate coefficient using the developed method. Additionally, we discuss a conceptually
simple and effective diabatization procedure for the calculation of pre-dissociated vibrational states for a system with ...
Comparison of density functionals for energy and structural
... approach to making a HPDF, Voorhis and Scuseria28 developed a Taylor series-like density matrix expansion to obtain
the so-called VSXC exchange-correlation functional29 which
has 21 parameters. It is in fact a meta-GGA, since it depends
not only on the density and its gradients but also on the
electron-proton nonadiabaticity: characterization
... expertise and will always be grateful for the time and patience shown to me, especially when I
was a younger graduate student just starting in the group. I thank her for allowing me the
opportunity to work on numerous interesting projects over the years, and for continually
encouraging me to explore ...
New Concepts in Inverse Quantum Chemistry - ETH E
... In this design procedure, we rely on density functional theory (DFT), which
is the only current quantum chemical theory capable of treating relatively large
systems at acceptable computational cost. The fact that the accuracy of a given
density functional for a particular molecular system cannot be ...
6 Chemical Bonding – Orbital Theory
... The orbitals containing a pair of electrons are not capable of combination. In fact, half-filled
orbitals on one atom have a tendency to combine with half-filled orbitals on other atom, and the
resulting orbital acquires a pair of electrons of opposite spins.
(2) The atoms with valence or bonding or ...
The Random Projection Method for Hyperbolic Systems with Stiff
... time scales. This can lead to problems of numerical stiffness. Even a stable (for example, with
an implicit source) scheme could lead to spurious numerical propagation speed when the
reaction time scale is not properly resolved numerically. This phenomenon was first observed
by Colella et al. , w ...
Tensor Product Methods and Entanglement
... The aim of the present paper is to give a pedagogical introduction to the theoretical background of this novel field and demonstrate the underlying benefits through numerical applications on
a text book example. We give a technical introduction to lowrank tensor factorization and do not intend to pr ...
Explicit Polarization Theory - Comp Chem
... approximated as a Hartree product of the wave functions of the individual fragments.
Consequently, the optimization of the total wave function can be reduced to the
optimization of each fragment embedded in and polarized by the rest of the system. Clearly,
variational optimization of the mutual depe ...
Relativistic effects in atomic and molecular properties
... Until the seventies of the 20th century it was generally accepted that for a description of the electronic structure of atoms and molecules and, therefore, for the whole chemistry and for the substantial part of physics, relativistic theory is not needed. According to Sheldon L. Glashow ,
Nobel P ...
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)↑ ↑