Complex Ground-State and Excitation Energies in Coupled-Cluster Theory

Since in coupled-cluster (CC) theory ground-state and excitation energies are eigenvalues of a non-Hermitian matrix, these energies can in principle take on complex values. In this paper we discuss the appearance of complex energy values in CC calculations from a mathematical perspective. We analyze the behaviour of the eigenvalues of Hermitian matrices that are perturbed (in a non-Hermitian manner) by a real parameter. Based on these results we show that for CC calculations with real-valued Hamiltonian matrices the ground-state energy generally takes a real value. Furthermore, we show that in the case of real-valued Hamiltonian matrices complex excitation energies only occur in the context…

Equation-of-motion coupled-cluster methods for atoms and molecules in strong magnetic fields.

A program for the direct calculation of excitation energies of atoms and molecules in strong magnetic fields is presented. The implementation includes the equation-of-motion coupled-cluster singles-doubles (EOM-CCSD) method for electronically excited states as well as its spin-flip variant. Differences to regular EOM-CCSD implementations are due to the appearance of the canonical angular-momentum operator in the Hamiltonian causing the wave function to become complex. The gauge-origin problem is treated by the use of gauge-including atomic orbitals. Therefore, a modified Davidson method for diagonalizing complex non-Hermitian matrices is used. Excitation energies for selected atoms and mole…

Erratum: “GW quasiparticle energies of atoms in strong magnetic fields” [J. Chem. Phys. 150, 214112 (2019)]

Full triples contribution in coupled-cluster and equation-of-motion coupled-cluster methods for atoms and molecules in strong magnetic fields

Coupled-cluster as well as equation-of-motion coupled-cluster methods play an important role whenever high accuracy is warranted. Concerning excitation energies, consideration of triple excitations is typically required to reach an accuracy better than 0.1–0.3 eV. In the context of strong magnetic fields such accuracy is needed for the prediction of spectra of strongly magnetized White Dwarfs. In addition it turns out that in order to correctly model the behavior of energies with respect to the magnetic field strength, triple excitations are required. Due to avoided crossings which are extremely often encountered in the context of strong magnetic fields, double-excitation character can be t…

GW quasiparticle energies of atoms in strong magnetic fields

Quasiparticle energies of the atoms H–Ne have been computed in the GW approximation in the presence of strong magnetic fields with field strengths varying from 0 to 0.25 atomic units (0.25 B 0 =0.25 ℏe −1 a −2 0 ≈58 763 0.25 B0=0.25 ℏe−1a0−2≈58 763 T). The GW quasiparticle energies are compared with equation-of-motion ionization-potential (EOM-IP) coupled-cluster singles-and-doubles (CCSD) calculations of the first ionization energies. The best results are obtained with the evGW@PBE0 method, which agrees with the EOM-IP-CCSD model to within about 0.20 eV. Ionization potentials have been calculated for all atoms in the series, representing the first systematic study of ionization potentials …

Transition-Dipole Moments for Electronic Excitations in Strong Magnetic Fields Using Equation-of-Motion and Linear Response Coupled-Cluster Theory

An implementation of transition-dipole moments at the equation-of-motion coupled-cluster singles-doubles (EOM-CCSD) and CCSD linear response (LR) levels of theory for the treatment of atoms and molecules in strong magnetic fields is presented. The presence of a finite magnetic field leads, in general, to a complex wave function and a gauge-origin dependence, necessitating a complex computer code together with the use of gauge-including atomic orbitals. As in the field-free case, for EOM-CC, the evaluation of transition-dipole moments consists of setting up the one-electron transition-density matrix (TDM) which is then contracted with dipole-moment integrals. In the case of CC-LR, the evalua…