Calculations of frequency-dependent properties by multiconfiguration time-dependent Hartree-Fock theory

Some theoretical and computational aspects of MC TDHF theory are analysed and two ways of solving the resulting equations are discussed. Numerical applications to the helium atom and the hydrogen molecule show that the frequency-dependent dipole polarizabilities can be obtained easily and with high accuracy in this approach. The polarizabilities at pure imaginary frequency are used to calculate the C ₆ coefficients for He-He, He-H₂ and H₂-H₂ interactions, also with high accuracy.     

Calculations of the Energies of the Excited States of Open-Shell Atoms in the Hartree-Fock Approximation

In the framework of the Roothaan-Hartree-Fock atomic theory, the solution of a many-electron problem is considered on the basis of the methods of minimizing a function of many variables. To implement this approach, expressions are obtained for the energy derivatives with respect to the elements of density matrices and the nonlinear parameters of atomic orbitals, that is, orbital exponents. Using the first- and second-order minimization methods, we performed optimization of the orbital exponents of Slater-type atomic orbitals for atoms and ions with several open shells. For them, energies that are close to the data of the numerical solution of the Hartree-Fock equations at a high accuracy of the virial ratio were determined. For a number of atoms the frequencies of the first dipole transitions were calculated, and the results were compared to the data obtained in calculation by the method of random phases and to experimental data. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 3, pp. 292–300, May–June, 2005.     

Internal conversion coefficients in the Hartree-Fock atomic model. Calculations and experiments for199Hg

The internal conversion coefficients were calculated for the transitions in¹⁹⁹Hg using both Hartree-Fock and Hartree-Fock-Slater atomic models. The relative conversion line intensities were measured with the magnetic spectrometers in Prague and Heidelberg. The multipolarities were determined to be:M1+(0.20±0.03)%E2, pure E2 and M 1+ (13.4 ±0.4)%E2 for the 50, 158 and 208 keV transitions, respectively. Allowing for the nuclear structure effect in M1 component we obtained: M1+(0.15±0.03) %E2,λ = 2.4±1.0 for the 50 keV and M1+ (10.9±0.7)% E2, λ=3.8±0.5 for the 208 keV transitions. Very good agreement was found between theory and experiment for the atomic subshells,K, L_1?3,M _1?5,N, andO + P.     

On the Photophysics of 3,5,6-Trichlorosalicylic Acid: Spectroscopic Study Combined with Hartree-Fock and Density Functional Theory Calculations

The present contribution reports a detailed photophysical study of a simple salicylic acid derivative viz., 3,5,6-Trichlorosalicylic acid (TCSA) based on steady state absorption, emission and time-resolved emission spectroscopy. Anomalous “dual” emission coupled with a large Stokes shift and negligible solvent polarity dependence marks the spectroscopic signature for Excited State Intramolecular Proton Transfer (ESIPT) reaction. Variation of medium polarity and pH of the medium have been implemented as fruitful tools to decipher the photophysics of TCSA. Quantum chemical calculation by ab initio Hartree-Fock and Density Functional Theory methods yields consistent results to follow experimental findings with distinct illustration of the inoperativeness of GSIPT reaction as well as occurrence of ESIPT process. A rigorous comparison of our experimental and theoretical measurements of TCSA with the parent compound salicylic acid, 5-chlorosalicylic acid and 3,5-dichlorosalicylic acid reveals the impact of chlorine substitution on the photophysics of the studied molecular systems with simultaneous exploration of the complexities induced in TCSA with respect to salicylic acid.     

Two-centre Hartree-Fock problems

Explorative Hartree-Fock calculations based on the two-centre oscillator Hamiltonian with a contact type residual force are carried out for the light systems ${}^8\text{Be}\text{2}{}^{\mathrm{<mtext>4</mtext><mtext>He</mtext>}}$ and ${}^{24}\text{Mg}\text{2}{}^{12}\text{C}$. Preliminary contact with experiment is made for the HF ground-state energies after correction for Coulomb and c.m. fluctuation effects. The single-particle spectra of the combined systems, which occur for a centre separation of 3.6 fm (⁸Be) and 2.8 fm (²⁴Mg) are compared to one-centre results.     

Directed polymers in Hartree-Fock approximation

A replica trick is used to map the problem of directed polymers into a quantum mechanics problem ofn-body bound states. This bound-state problem is then treated using a self-consistent method of Hartree-Fock. Ford=2, the exact result of the DP exponents is reproduced; and for complex DP, the ground-state energyE _n n² is found, confirming previous numerical results.     

Multi-configuration Hartree-Fock theory in nuclei

A variational method for the self-consistent solution of the nuclear many body problem with the inclusion of correlations is formulated. The trial function in this multiconfiguration-Hartree-Fock (MCHF) theory is a linear combination of unrestricted Slater determinants. The MCHF equations are given and a simple procedure for solving them is outlined. A great advantage of this method is that it also yields the excited states. It is shown that the trial function is stable against particle-hole excitations. Therefore the Slater determinants differ from each other at least by two particle — two hole excitations. This method is applied to the Lipkin model. In the MCHF method the difference to the exact solution is reduced by a factor three to ten compared with the corresponding value in the HF approach.     

Mapping exchange in relativistic Hartree-Fock

We show that formally for the standard ansatz relativistic point-coupling mean-field (RMF-PC) model a Lagrangian density is not equivalent in Hartree and Hartree-Fock approximations. The equivalency can be achieved only if we use a “complete” ansatz at the cost of introducing new parameters in the model. An approximate treatment of the exchange terms from standard RMF-PC indicates that these effects cannot be easily, if at all, absorbed by a Dirac-Hartree approximation.     

Coupled Cluster Method Calculations of Quantum Magnets with Spins of General Spin Quantum Number

We present a new high-order coupled cluster method (CCM) formalism for the ground states of lattice quantum spin systems for general spin quantum number, s. This new general-s formalism is found to be highly suitable for a computational implementation, and the technical details of this implementation are given. To illustrate our new formalism we perform high-order CCM calculations for the one-dimensional spin-half and spin-one antiferromagnetic XXZ models and for the one-dimensional spin-half/spin-one ferrimagnetic XXZ model. The results for the ground-state properties of the isotropic points of these systems are seen to be in excellent quantitative agreement with exact results for the special case of the spin-half antiferromagnet and results of density matrix renormalization group (DMRG) calculations for the other systems. Extrapolated CCM results for the sublattice magnetization of the spin-half antiferromagnet closely follow the exact Bethe Ansatz solution, which contains an infinite-order phase transition at =1. By contrast, extrapolated CCM results for the sublattice magnetization of the spin-one antiferromagnet using this same scheme are seen to go to zero at 1.2, which is in excellent agreement with the value for the onset of the Haldane phase for this model. Results for sublattice magnetizations of the ferrimagnet for both the spin-half and spin-one spins are non-zero and finite across a wide range of , up to and including the Heisenberg point at =1.     

Time-dependent Hartree-Fock theory

The lowest singlet and triplet excited states of the two paired electrons in a chemical bond are treated by the time-dependent Hartree-Fock (H.F.) method, with the π electrons of the double bond in ethylene as an example. The results depend on a dimensionless parameter g which describes the strength of the electron correlation effects, and they are compared with a simple configuration interaction calculation. When g is small the frequencies and amplitudes of the Hartree-Fock oscillations give an accurate estimate of the energies and intensities of the two lowest transitions, the correlation energy and the pair distribution function of the gound state. The correlation energy is related to the zero-point energy of the oscillations. As g increases the H.F. method overestimates the correlation corrections and breaks down completely if g = 1. At this point the triplet oscillation becomes unstable, because the molecular orbital wave-function with two paired electrons ceases to be the state of lowest energy. When g is large the H.F. results violate spin conservation and the exclusion principle.     

Thermodynamic Hartree-Fock approximation in fermi systems

Bogoliubov's variational principle is applied to a test Hamiltonian operator in Hartree-Fock approximation. The extremal conditions are proven to be identical with self-consistent equations for Green's functions.     

High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States

In this article, we prove that exact representations of dimer and plaquette valence-bond ket ground states for quantum Heisenberg antiferromagnets may be formed via the usual coupled cluster method (CCM) from independent-spin product (e.g. Néel) model states. We show that we are able to provide good results for both the ground-state energy and the sublattice magnetization for dimer and plaquette valence-bond phases within the CCM. As a first example, we investigate the spin-half J ₁–J ₂ model for the linear chain, and we show that we are able to reproduce exactly the dimerized ground (ket) state at J ₂/J ₁=0.5. The dimerized phase is stable over a range of values for J ₂/J ₁ around 0.5, and results for the ground-state energies are in good agreement with the results of exact diagonalizations of finite-length chains in this regime. We present evidence of symmetry breaking by considering the ket- and bra-state correlation coefficients as a function of J ₂/J ₁. A radical change is also observed in the behavior of the CCM sublattice magnetization as we enter the dimerized phase. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the Néel and the dimerized phases. Once again, very good results for the ground-state energies are obtained. We find CCM critical points of the bra-state equations that are in agreement with the known phase transition point for this model. The results for the sublattice magnetization remain near to the “true” value of zero over much of the dimerized regime, although they diverge exactly at the critical point. Finally, we consider a spin-half system with nearest-neighbor bonds for an underlying lattice corresponding to the magnetic material CaV₄O₉ (CAVO). We show that we are able to provide excellent results for the ground-state energy in each of the plaquette-ordered, Néel-ordered, and dimerized regimes of this model. The exact plaquette and dimer ground states are reproduced by the CCM ket state in their relevant limits. Furthermore, we estimate the range over which the Néel order is stable, and we find the CCM result is in reasonable agreement with the results obtained by other methods. Our new approach has the dual advantages that it is simple to implement and that existing CCM codes for independent-spin product model states may be used from the outset. Furthermore, it also greatly extends the range of applicability to which the CCM may be applied. We believe that the CCM now provides an excellent choice of method for the study of systems with valence-bond quantum ground states.     

The Hartree-Fock seniority approximation

A new self-consistent method is used to take into account the mean-field and the pairing correlations in nuclei at the same time. We call it the Hartree-Fock seniority approximation, because the long-range and short-range correlations are treated in the frameworks of Hartree-Fock theory and the seniority scheme. The method is developed in detail for a minimum-seniority variational wave function in the coordinate representation for an effective interaction of the Skyrme type. An advantage of the present approach over the Hartree-Fock-Bogoliubov theory is the exact conservation of angular momentum and particle number. Furthermore, the computational effort required in the Hartree-Fock seniority approximation is similar to that of the pure Hartree-Fock picture. Some numerical calculations for Ca isotopes are presented.     

Variational time-dependent Hartree-Fock calculations

A pseudopotential framework is used to develop a simplified version of time-dependent Hartree-Fock theory. Variational solutions of the equations are obtained for the alkali metal hydrides LiH, NaH and KH, and excitation energies, oscillator strengths and other properties are calculated. The results are in good agreement with more elaborate theoretical calculations.     

The unrestricted Hartree-Fock method

The unrestricted Hartree-Fock method is important for discussing several effects, including the spin density produced in the core of an atom by exchange with an unfilled valence electron shell. The method allows electrons with and spins to have slightly different orbitals due to the differing exchange interaction, but ignores the fact that this automatically results in gaining also some in-out correlation energy. The validity of the method must therefore be questioned, since correlation is in general the larger effect. It is shown that in atomic calculations the method gives results which are in fact correct to a good order of approximation. However, the interplay of spin polarisation and correlation is such that in some molecular or other systems the method would fail.     

Gluon magnetic mass in Hartree-Fock approximation

It is shown that generation of a mass for spatial gluons is possible at finite temperature and chemical potential when a Hartree-Fock approximation is made in the equations of motion for the generating functional. The asymptotic expression for this magnetic mass is estimated in the range of validity of the approximation and it turns out to be $\text{O}\text{(g}\text{ln}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(μ/μ}{}_0\text{))}$.     

The Hartree-Fock lane potential

The charge exchange potential has been determined microscopically starting from two-body forces and totally anti-symmetrized wavefunctions. The results for ${}^{48}\text{Ca}$, p scattering are given in fig 1.     

Ab-initio effective potentials in crystal Hartree-Fock theory

Ab initio effective potential technique of Ewiget al is applicable directly to crystal Hartree-Fock formalism provided the effective potentials are suitably defined. Corresponding to every atom or every molecule by constructing a crystal one can assign a unit species configuration. The effective potentials in the crystal can be expressed as functions of lattice parameters in terms of integrals over the orbitals of this unit species. These expressions are in a more exact form than those usually employed in molecular calculations.     

Improved uncoupled Hartree-Fock perturbation theory

Various uncoupling schemes used in the first-order Hartree-Fock perturbation theory are compared. The analysis and extraction of the most important terms in the coupled Hartree-Fock perturbation scheme leads to a definition of the new functional for the determination of the first-order perturbed orbitals. This new functional represents an alternative uncoupling scheme for the first-order Hartree-Fock perturbation theory. Some special cases of real and pure imaginary perturbations and also the connections with previously proposed uncoupling schemes are discussed.

The uncoupling procedure proposed in this paper is illustrated by electric dipole polarizability calculations for some Be- and Ne-like atomic systems. The results obtained are almost as good as those calculated by using coupled Hartree-Fock perturbation theory.