Fock-space Coupled Cluster Method Research Articles

On multiple solutions of the Fock-space coupled-cluster method

Intermediate Hamiltonian techniques are used to investigate the problem of multiple solutions of the Fock-space coupled-cluster methods. Two intermediate Hamiltonian schemes are presented, based upon similarity transformations that unlike the wave operator formalism allow for following the complete eigenvalue problem. Solutions of the standard effective Hamiltonian formulation that requires iterative approaches to solve the equations are equivalently given by diagonalization of the intermediate Hamiltonian matrix representations. This procedure provides a systematic way of obtaining all possible solutions of the effective Hamiltonian scheme in all sectors higher than the lowest one.

Transition energies of ytterbium, lutetium, and lawrencium by the relativistic coupled-cluster method.

The relativistic Fock-space coupled-cluster method was applied to the Yb, Lu, and Lr atoms, and to several of their ions. A large number of transition energies was calculated for these systems. Starting from an all-electron Dirac-Fock or Dirac-Fock-Breit function, many electrons (30--40) were correlated to account for core-valence polarization. High-l virtual orbitals were included (up to l=5) to describe dynamic correlation. Comparison with experiment (when available) shows agreement within a few hundred wave numbers in most cases. Fine-structure splittings are even more accurate, within 30 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ of experiment. Average errors are at least three times smaller than for previous calculations. Two bound states of ${\mathrm{Lu}}^{\mathrm{\ensuremath{-}}}$ are predicted, 6p5d $^{1}$${\mathit{D}}_{2}$ and 6${\mathit{p}}^{2}$ $^{3}$${\mathit{P}}_{0}$, with binding energies of about 2100 and 750 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, respectively. The ground state of lawrencium is $^{2}$${\mathit{P}}_{1/2}$, relativistically stabilized relative to $^{2}$${\mathit{D}}_{3/2}$, the ground state of Lu. Two states of the ${\mathrm{Lr}}^{\mathrm{\ensuremath{-}}}$ anion are bound, 7${\mathit{p}}^{2}$ $^{3}$${\mathit{P}}_{0}$ (by 2500 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) and 7p6d $^{1}$${\mathit{D}}_{2}$ (by 1300 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$).

Relativistic coupled-cluster method: Intrashell excitations in the f2 shells of Pr+3 and U+4.

The relativistic Fock-space coupled-cluster method for the direct calculation of ionization potentials and excitation energies (including fine structure) is applied to the 4${\mathit{f}}^{2}$ levels of ${\mathrm{Pr}}^{+3}$ and the 5${\mathit{f}}^{2}$ levels of ${\mathrm{U}}^{+4}$. The no-pair Dirac-Coulomb-Breit Hamiltonian is taken as the starting point. Correlation is treated by the coupled-cluster singles-and-doubles approximation, which includes single and double virtual excitations in a self-consistent manner, incorporating therefore the effects of the Coulomb and Breit interactions to all orders in these excitations. Extensive basis sets of kinetically balanced four-component Gaussian spinors are used to span the atomic orbitals. All levels appear in correct order. The average error of the excitation energies with the best basis is 222 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for ${\mathrm{Pr}}^{+3}$ and 114 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for ${\mathrm{U}}^{+4}$. Fine-structure splittings are obtained with even better accuracy.

Relativistic all-electron coupled-cluster calculations on the gold atom and gold hydride in the framework of the douglas-kroll transformation

A one-component relativistic method, based on the Douglas-Kroll transformation, is combined with the Fock-space coupledcluster method for treating electron correlation. The method is applied to the gold atom, the AuH molecule, and their ions. Excitation energies, ionization potentials, electron affinities and bond energies are calculated. Good agreement with experiment is obtained.

Ionization potentials and excitation energies of the alkali-metal atoms by the relativistic coupled-cluster method.

Ground- and excited-state energies, as well as ionization potentials and electron affinities, are calculated for all the alkali-metal atoms Li--Fr by the relativistic Fock-space coupled-cluster method. The coupled-cluster singles and doubles approximation, which includes single and double virtual excitations in a self-consistent manner, is implemented. The no-pair Dirac-Coulomb-Breit Hamiltonian is taken as the starting point. Rather extensive basis sets of balanced Gaussian spinors are used to span the atomic orbitals. The average error for the ionization potentials is 0.09% and for excitation energies 0.2%. Electron affinities are less accurate, particularly for the heavier atoms, with errors of 4--9 % for K, Rb, and Cs.

Open-shell relativistic coupled-cluster method with Dirac-Fock-Breit wave functions: Energies of the gold atom and its cation

The relativistic Fock-space coupled cluster method for the direct calculation of ionization potentials and excitation energies (including fine structure) is presented and applied to atomic Au and its ions. The no-pair Dirac-Coulomb-Breit Hamiltonian is taken as the starting point. The CCSD approximation is implemented (where CCSD indicates coupled cluster with single and double excitations), which includes single and double virtual excitations in a self-consistent manner, incorporating therefore the effects of the Coulomb and Breit interactions to all orders in these excitations. A rather large basis set (21s17p11d7f) of kinetically balanced Gaussian spinors is used to span the atomic orbitals. All calculated energies (ionization potential and electron affinity of Au, excitation energies of Au and ${\mathrm{Au}}^{+}$) agree with experiment to 0.1 eV or better, with an average error of 0.06 eV. Fine-structure splittings are accurate to better than 0.01 eV.

The Fock-space coupled-cluster method: Electron affinities of the five halogen elements with consideration of triple excitations

The Fock-space coupled-cluster method with single and double excitations (CCSD or SUB2) is applied to the calculation of the electron affinities of all five halogen elements, F–At. Excellent agreement with experiment is obtained, the average error being 0.04 eV. The inclusion of triple excitations for F and Cl spoils the agreement. Comparison with other methods is made.

Electron propagator theory with the ground state correlated by the coupled-cluster method

Ground state electron correlation is introduced into the one-particle propagator via coupled cluster theory. This defines a similarity transformation of the Hamiltonian, which leads to the complete separation of the ionization and electron attachment aspects of the propagator. The latter makes it possible to solve for each property independently. Furthermore, the frequency (or energy) dependence which characterizes propagator theory is eliminated by introducing a wave operator formalism. It is shown that this procedure is equivalent to the summation of certain types of terms in the electron propagator perturbation expansion to infinite order. Finally, the resulting equations are found to be equivalent to those of the Fock-space coupled-cluster (or equivalently the equation of motion coupled-cluster) method, which provides an explicit wave function for each state, demonstrating the connection between these different approaches for the calculation of ionization potentials and electron affinities. Understanding this relationship permits new and powerful approximations to be proposed. © 1993 John Wiley & Sons, Inc.

Coupled-cluster reference electron propagator calculations on the ionization energies of O 2

Electron propagator calculations of various levels are compared with coupled-cluster and Fock-space coupled-cluster methods on O 2 ionization energies where final states are dominated by a single configuration. Among the electron propagator method is an approximation that employs correlations to reference state density matrices from a coupled-cluster singles and doubles calculation. The closest agreement between the two classes of methods occurs between renormalized electron propagator approximations and the Δ coupled-cluster singles and doubles method,e ven though the latter is not, like the Fock-space methods, a direct method for ionization energies. Basis set effects are also examined. Vertical ionization energies within 0.2 eV of experiment obtain with the coupled-cluster reference electron propagator calculations

High sectors in the Fock space coupled-cluster method

The coupled-cluster method with single and double excitations (CCSD or full SUB2) is applied to systems with n electrons outside a closed shell, n⩽6. The CCSDT1 scheme, which includes triple excitations approximately, is also employed. The systems of interest are the F atom and its ions. F 5+ is the reference state, and the ionization potentials and excitation energies involving the 2p and 3s electrons are calculated. The CCSD results are good for n=1 and 2, but deteriorate with increasing n. The CCSDT1 scheme gives satisfactory results in the n=3 and 4 sectors, but overestimates the effects for higher n.

Fock-space coupled-cluster method

A generalization of the single-reference coupled-cluster method, employing the algebraic properties of the fermionic Fock space, is presented. This Fock-space coupled-cluster (FSCC) method is capable of providing not only the ground-state energy of anN-electron system, but also an important fraction of system's excitation spectrum, including ionization potentials, electron affinities, and excitation energies corresponding toN-electron singlet and triplet states. The FSCC method is applied to study the electronic spectra corresponding to the Pariser-Parr-Pople model of butadiene, hexatriene, and benzene, with the full configuration-interaction results taken as the reference. The problem of intruder states is discussed.

The Fock space coupled cluster method: theory and application

The Fock space coupled cluster method and its application to atomic and molecular systems are described. The importance of conserving size extensivity is demonstrated by the electron affinities of the alkali atoms. Two types of intruder states are discussed, one attributable to the orbital energy spectrum and the other caused by two-electron interactions. They are illustrated by the excited states of Li2 and by1S states of Be, respectively. It is shown how both problems may be solved using incomplete model spaces. The selection of the model space in a moderately dense spectrum is discussed in connection with N2 excited states.