Arie Landau

Intermediate Hamiltonian Fock-space coupled-cluster method: Excitation energies of barium and radium

An intermediate Hamiltonian Fock-space coupled cluster method is introduced, based on the formalism developed by Malrieu and co-workers in the context of perturbation theory. The method is designed to make possible the use of large P spaces while avoiding convergence problems traceable to intruder states, which often beset multireference coupled cluster schemes. The essence of the method is the partitioning of P into a main Pm and an intermediate Pi serving as buffer, with concomitant definition of two types of wave and excitation operators. Application to atomic barium and radium yields converged results for a large number of states not accessible by traditional Fock-space coupled cluster. Moreover, states calculated by both methods exhibit better accuracy (by a factor of 2–5) in the intermediate Hamiltonian approach. Energies are given for low-lying states of Ra which have not been observed experimentally.

Electronic Structure and Spectroscopy of Nucleic Acid Bases: Ionization Energies, Ionization-Induced Structural Changes, and Photoelectron Spectra

We report high-level ab initio calculations and single-photon ionization mass spectrometry study of ionization of adenine (A), thymine (T), cytosine (C), and guanine (G). For thymine and adenine, only the lowest-energy tautomers were considered, whereas for cytosine and guanine we characterized the five lowest-energy tautomeric forms. The first adiabatic and several vertical ionization energies were computed using the equation-of-motion coupled-cluster method for ionization potentials with single and double substitutions. Equilibrium structures of the cationic ground states were characterized by DFT with the ωB97X-D functional. The ionization-induced geometry changes of the bases are consistent with the shapes of the corresponding molecular orbitals. For the lowest-energy tautomers, the magnitude of the structural relaxation decreases in the following series, G > C > A > T, the respective relaxation energies being 0.41, 0.32, 0.25, and 0.20 eV. The computed adiabatic ionization energies (8.13, 8.89, 8.51-8.67, and 7.75-7.87 eV for A, T, C, and G, respectively) agree well with the onsets of the photoionization efficiency (PIE) curves (8.20 ± 0.05, 8.95 ± 0.05, 8.60 ± 0.05, and 7.75 ± 0.05 eV). Vibrational progressions for the S(0)-D(0) vibronic bands computed within double-harmonic approximation with Duschinsky rotations are compared with previously reported experimental photoelectron spectra and differentiated PIE curves.

New implementation of high‐level correlated methods using a general block tensor library for high‐performance electronic structure calculations

This article presents an open‐source object‐oriented C++ library of classes and routines to perform tensor algebra. The primary purpose of the library is to enable post‐Hartree–Fock electronic structure methods; however, the code is general enough to be applicable in other areas of physical and computational sciences. The library supports tensors of arbitrary order (dimensionality), size, and symmetry. Implemented data structures and algorithms operate on large tensors by splitting them into smaller blocks, storing them both in core memory and in files on disk, and applying divide‐and‐conquer‐type parallel algorithms to perform tensor algebra. The library offers a set of general tensor symmetry algorithms and a full implementation of tensor symmetries typically found in electronic structure theory: permutational, spin, and molecular point group symmetry. The Q‐Chem electronic structure software uses this library to drive coupled‐cluster, equation‐of‐motion, and algebraic‐diagrammatic construction methods.

Frozen natural orbitals for ionized states within equation-of-motion coupled-cluster formalism

The frozen natural orbital (FNO) approach, which has been successfully used in ground-state coupled-cluster calculations, is extended to open-shell ionized electronic states within equation-of-motion coupled-cluster (EOM-IP-CC) formalism. FNOs enable truncation of the virtual orbital space significantly reducing the computational cost with a negligible decline in accuracy. Implementation of the MP2-based FNO truncation scheme within EOM-IP-CC is presented and benchmarked using ionized states of beryllium, dihydrogen dimer, water, water dimer, nitrogen, and uracil dimer. The results show that the natural occupation threshold, i.e., percentage of the total natural occupation recovered in the truncated virtual orbital space, provides a more robust truncation criterion as compared to the fixed percentage of virtual orbitals retained. Employing 99%-99.5% natural occupation threshold, which results in the virtual space reduction by 70%-30%, yields errors below 1 kcal/mol. Moreover, the total energies exhibit linear dependence as a function of the percentage of the natural occupation retained allowing for extrapolation to the full virtual space values. The capabilities of the new method are demonstrated by the calculation of the 12 lowest vertical ionization energies (IEs) and the lowest adiabatic IE of guanine. In addition to IE calculations, we present the scans of potential energy surfaces (PESs) for ionized (H(2)O)(2) and (H(2))(2). The scans demonstrate that the FNO truncation does not introduce significant nonparallelity errors and accurately describes the PESs shapes and the corresponding energy differences, e.g., dissociation energies.

Electronic structure of eka-lead (element 114) compared with lead

The electronic level structure of eka-lead (element 114), the synthesis of which was reported last year, is studied by the recently developed intermediate Hamiltonian Fock-space coupled-cluster method. Very large basis sets are used, with l up to 8, and 36 electron are correlated. The accuracy of the resulting transition energies is tested by applying the same method to Pb; calculated ionization potentials and excitation energies agree with experiment within a few hundredths of an eV, and similar accuracy is expected for the heavier element. Ionization potentials and excitation energies of E114 are considerably higher than for Pb, due to the relativistic stabilization of the 7s and 7p1/2 orbitals. This indicates that eka-lead will probably be more inert and less metallic than lead.

Mixed-sector intermediate Hamiltonian Fock-space coupled cluster approach.

An alternative formulation of the intermediate Hamiltonian Fock-space coupled cluster scheme developed before is presented. The methodological and computational advantages of the new formulation include the possibility of using a model space with determinants belonging to different Fock-space sectors. This extends the scope of application of the multireference coupled cluster method, and makes possible the use of quasiclosed shells (e.g., p2, d4) as reference states. Representative applications are described, including electron affinities of group-14 atoms, ionization potentials of group-15 elements, and ionization potentials and excitation energies of silver and gold. Excellent agreement with experiment (a few hundredths of an electronvolt) is obtained, with significant improvement (by a factor of 5-10 for p3 states) over Fock-space coupled cluster results. Many states not reachable by the Fock-space approach can now be studied.

Intermediate Hamiltonian Fock-space coupled cluster method in the one-hole one-particle sector: Excitation energies of xenon and radon

The intermediate Hamiltonian Fock-space coupled cluster method developed recently is applied to excitations in the one-hole one-particle sector, taking xenon and radon atoms as test cases. Virtual orbitals are modified to yield better approximations to orbitals occupied in excited states. The usual Fock-space coupled cluster scheme diverges for these systems, but the intermediate Hamiltonian approach converges for large P spaces and yields excitation energies in very good agreement with experiment. The average error in the calculated values for the lowest excitation energies (about 20 for each atom) is 0.6%. Predictions are made for the unobserved 8s Rydberg states of Rn.

Benchmark calculations of electron affinities of the alkali atoms sodium to eka-francium (element 119)

Electron affinities of the alkali atoms sodium to eka-francium are calculated by the intermediate Hamiltonian Fock-space coupled cluster approach, which allows very large P spaces. Large basis sets are used (37s32p23d18f10g7h for most atoms), and many electrons are correlated (from 10 for Na− to 52 for E119−) to account for core polarization. While the usual Fock-space method gives errors of 5%–9% for K, Rb, and Cs, the intermediate Hamiltonian results agree with all known values to 5 meV or 1%. The EA of Fr, not known experimentally, is predicted at 491±5 meV. While EAs decrease from Li to Cs, the Fr value is 20 meV higher than that of Cs, with E119 EA being much higher at 662 meV. This trend reversal is due to relativistic stabilization of s orbitals, which has been shown [Eliav et al., Phys. Rev. Lett. 74, 1079 (1995)] to give the rare gas E118 positive electron affinity.

Intermediate Hamiltonian Fock-space coupled-cluster method

An intermediate Hamiltonian Fock-space coupled cluster method is introduced, based on the formalism developed by Malrieu and coworkers in the context of perturbation theory. The method is designed to make possible the use of large P spaces while avoiding convergence problems traceable to intruder states, which often beset multi-reference coupled cluster approaches. The essence of the method is the partitioning of P into a main Pm and an intermediate Pi serving as buffer, with concomitant definition of two types of wave and excitation operators. While Malrieus formulation eliminated Pm → Pi transitions up to third order only, the requirement introduced here that Pm → Q amplitudes of the two excitation operators be equal makes possible an all-order method without these dangerous transitions. This requirement is shown to be satisfied for sufficiently large Pi. Application to atomic barium and radium yields converged results for a large number of states not accessible by traditional Fock-space coupled cluster. Moreover, states calculated by both methods exhibit better accuracy (by a factor of 2–5) in the intermediate Hamiltonian approach. Excellent agreement with experiment (better than 0.01 eV) is obtained for the electron affinities of alkali atoms, and excitation energies of Xe and Rn, not accessible by the traditional coupled-cluster Fock-space method, are calculated showing high accuracy.

Electronic structure of eka-thorium (element 122) compared with thorium

The electronic levels of thorium and eka-thorium (element 122) are calculated in the framework of the Dirac-Coulomb-Breit Hamiltonian using a large Gaussian-spinor basis. Correlation is included by the Fock-space or intermediate Hamiltonian coupled-cluster method. The 51 reported levels of thorium and its ions are compared with experiment, giving an average error of 0.062 V for Fock space and 0.051 V for the intermediate Hamiltonian method. Predicted E122 levels are expected to have similar accuracy. The ground state of E122 is 8s27d8p, to be contrasted with 7s26d2 for Th. Increased relativistic effects in the super-heavy element lead to major differences between the level structure of these two atoms and their ions. The effects of Breit and QED terms are discussed.