Coupled cluster method ionization potentials

Energy levels of heavy and super-heavy (Z>100) elements are calculated by the relativistic coupled cluster method. The method starts from the four-component solutions of the Dirac-Fock or Dirac-Fock-Breit equations, and correlates them by the coupled-cluster approach. Simultaneous inclusion of relativistic terms in the Hamiltonian (to order o , where a is the fine-structure constant) and correlation effects (all products smd powers of single and double virtual excitations) is achieved. The Fock-space coupled-cluster method yields directly transition energies (ionization potentials, excitation energies, electron affinities). Results are in good agreement (usually better than 0.1 eV) with known experimental values. Properties of superheavy atoms which are not known experimentally can be predicted. Examples include the nature of the ground states of elements 104 md 111. Molecular applications are also presented. 

M. Rittby and R.. Bartlett,/. Phys. Chem., 92, 3033 (1988). An Open-Shell Spin-Restricted Coupled-Cluster Method Application to Ionization Potentials in N2. 

Equations for the Fock space coupled cluster method, including all single, double, and triple excitations (FSCCSDT) for ionization potentials [(0,1) sector], are presented in both operator and spin orbital form. Two approximations to the full FSCCSDT equations are described, one being the simplest perturbative inclusion of triple excitation effects, FSCCSD+T(3), and a second that indirectly incorporates certain higher-order effects, FSCCSD+T (3). 

Multireference coupled cluster methods, which started development more recently, are generally divided into two types. Hilbert space CC methods use multiple reference functions to obtain a description of a few states, including the reference state (for a review see (4)). Fock space methods (for a review see (5)), on the other hand, provide direct state-to-state energy differences, relative to some common reference state. The Fock space approach is particularly well-suited to the calculation of ionization potentials (IPs), electron affinities (EAs), and excitation energies (EEs). For principal IPs and EAs, FSCC is equivalent (6, 7) to the EOM-IP and EOM-EA CC methods (1, 2, 7, 8). In this paper, we will focus primarily on the IP problem. 

S. Pal, M. Rittby, and R. J. Bartlett, Chem. Phys. Lett., 160, 212 (1989). Multi-Reference Coupled-Cluster Methods of Ionization Potentials with Partial Inclusion of Triple Excitations. 

A Fock space multireference coupled cluster method was described by Rittby and Bartlett <91TCA469>, applied to the calculation of ionization potentials and excitation energies of 1,2,4,5-tetrazines, and compared with conventional ab initio calculations and experimental results. 

Pal, S., Rittby, M., Bartlett, R. J., Sinha, D., Mukherjee, D. [1987]. Multireference Coupled-Cluster Methods Using an Incomplete Model Space Application to Ionization Potentials and Excitation Energies of Formaldehyde, Chem. Phys. Lett, 137, 272-27Q. 

Abstract The singlet-triplet splittings of the di-radicals methylene, trimethylene-methane, ortha-, meta- and para-benzynes, and cyclobutane-l,2,3,4-tetrone have become test systems for the applications of various multi-reference (MR) coupled-cluster methods. We report results close to the basis set limit computed with double ionization potential (DIP) and double electron attachment (DBA) equation-of-motion coupled-cluster methods. These diradicals share the characteristics of a 2-hole 2-particle MR problem and are commonly used to assess the performance of MR methods, and yet require more careful study unto themselves as benchmarks. Here, using our CCSD(T)/6-311G(2d,2p) optimized geometries, we report DIP/DEA-CC results and single-reference (SR) CCSD, CCSD(T), ACCSD(T) and CCSDT results for comparison. 

The ionization potentials and electron affinities of the atoms H, C, N, O and F have been computed by means of coupled-cluster methods using doubly augmented correlation-consistent one-electron basis sets in conjunction with explicitly correlated Slater-type geminals. Excitations up to the level of connected quintuples have been accounted for, and all orbitals in the core and valence shells have been correlated. Relativistic effects (spin-orbit as well as scalar) and diagonal Born-Oppenheimer corrections have been included. 

The electron affinities and ionization potential of the H, C, N, O and F atoms were computed by using conventional coupled-cluster methods supplemented with the explicitly correlated treatment at the CCSD(F12) level of theory. Agreement with experimental values of the order of magnitude of a fraction of meV was reached for hydrogen, carbon and nitrogen. 

E. Eliav, U. Kaldor, and Y. Ishikawa, Ionization potentials and excitation energies of the alkali-metal atoms by the relativistic coupled cluster method, Phys. Rev. A 50, 1121 (1994). 

It is well known that electron correlation plays a key role in understanding the most interesting phenomena in molecules. It has been the focal point of atomic and molecular theory for many years [1] and various correlated methods have been developed [2]. Among them are many-body perturbation theory [3] (MBPT) and its infinite-order generalization, coupled cluster (CC) theory [4,5], which provides a systematic way to obtain the essential effects of correlation. Propagator [6-9] or Green s function methods (GFM) [10-14] provide another correlated tool to calculate the electron correlation corrections to ionization potentials (IPs), electron affinites (EAs), and electronic excitations. 

Balabanov, N.B., Peterson, K.A. Basis set limit electronic excitation energies, ionization potentials, and electron affinities for the 3d transition metal atoms Coupled cluster and multireference methods, J. Chem. Phys. 2006,125,074110. 

The ionization potentials and electron affinities of the H, C, N, O and F atoms have been computed by means of state-of-the-art electronic structure methods. The conventional coupled-cluster calculations were performed up to the connected pentuple excitation level. For the purpose of the basis set truncation correction the implementation of the CCSD(F12) model in Turbomole was applied. Final results were supplemented with relativistic and diagonal Born-Oppenheimer corrections. Estimated values of the IPs and EAs are in good agreement with the experimental values and the deviations do not exceed 0.7 meV, in the cases of H, C and N atoms and the IP of O atom. The results obtained for fluorine differ by ca. 1 and 5 meV from the experiment, respectively for the IP and EA. The EA of oxygen is plagued with discrepancy that amounts to ca. 4 meV. 

It was seen in Section 5.3 that to determine the QP band structures of a polymeric chain one must use a size-consistent method to determine the major part of the correlation [many-body perturbation theory (MBPT) in the Moller-Plesset partitioning, coupled-cluster theory, etc.]. Suhai, in his QP band-structure calculation on polyacetylenes and polydiace-tylenes, used second-order (MP/2) Moller-Plesset MBPT. For polydiacetylenes he obtained 5.7 eV as first ionization potential (using the generalized Koopmans theorem) for the PTS structure (see Figure 8.1), in reasonable agreement with experiment (A = 5.5 0.1 while the HF value (the simple Koopmans theorem) is 6.8 eV.< > For the TCDU diacetylene structure the theoretical value is 5.0 eV (HF value, 6.2 eV). Unfortunately, there is no reliable experimental ionization-potential value available for the TCDU structure of polydiacetylene. 

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