The cyclic cluster model at hartree–fock level

We present the implementation of the cyclic cluster model (CCM) formalism at the Hartree–Fock (HF) level. In contrast to other periodic models, the CCM is a Γ‐point approach. Integration is carried out in real space within a finite interaction area determined by the size and the shape of the cluster that corresponds to a supercell of the solid, surface, or polymer. Particular care has to be taken for the proper treatment of three‐ and four‐center integrals that involve basis functions located at the boundaries of the Wigner–Seitz supercell, which defines the interaction region. The similarity between the CCM formalism and molecular approaches allows in principle the application of sophisticated post HF methods to solid‐state problems with only moderate modification of the molecular code. We show for selected model systems, that with our approach, the electronic structure and energetics obtained by the conventional supercell model is fully reproduced. © 2014 Wiley Periodicals, Inc.     

Optimization of molecular electronic structure calculations. 1. Local symmetry and local symmetricized orbitals

A formalism is suggested of the so-called local symmetricized orbitals to be used for the construction of a symmetricized basis in molecular electronic structure calculations. The local symmetricized orbitals are defined as additive contributions to the symmetry orbitals of a molecule that arise from symmetry operations of a corresponding atom. The local symmetricized orbitals are transformed according to the irreducible representations of the molecular symmetry group. This approach appears to be most suitable for the optimization of quantum mechanical calculations accounting for the spatial symmetry of compounds under consideration. This fact is due to the formalism of the local symmetricized orbitals that explicitly accounts for the local symmetry of basis function centers, which is essential for such optimization.     

Periodic calculations of excited state properties for solids using a semiempirical approach

The semiempirical SCF MO method MSINDO (modified symmetrically orthogonalized intermediate neglect of differential overlap) [T. Bredow and K. Jug, Electronic Encyclopedia of Computational Chemistry, 2004] is extended to the calculation of excited state properties through implementation of the configuration interaction singles (CIS) approach. MSINDO allows the calculation of periodic systems via the cyclic cluster model (CCM) [T. Bredow et al., J. Comput. Chem., 2001, 22, 89] which is a direct-space approach and therefore can be in principle combined with all molecular quantum-chemical techniques. The CIS equations are solved for a cluster with periodic boundary conditions using the Davidson-Liu iterative block diagonalization approach. As a proof-of-principle, MSINDO-CCM-CIS is applied for the calculation of optical spectra of ZnO and TiO(2), oxygen-defective rutile, and F-centers in NaCl. The calculated spectra are compared to available experimental and theoretical literature data. After re-adjustment of the empirical parameters the quantitative agreement with experiment is satisfactory. The present approximate approach is one of the first examples of a quantum-chemical methodology for solids where excited states are correctly described as n-electron state functions. After careful benchmark testing it will allow calculation of photophysical and photochemical processes relevant to materials science and catalysis.     

On the ground state of Pd13

First-principles electronic structure calculations within a gradient corrected density functional formalism have been carried out to investigate the electronic structure and magnetic properties of Pd(13) clusters. It is shown that a bilayer ground-state structure that can be regarded as a relaxed bulk fragment is most compatible with the experimental results from Stern-Gerlach measurements. An icosahedral structure, considered to be the ground state in numerous previous studies, is shown to be around 0.14 eV above the ground state. A detailed analysis of the molecular orbitals reveals the near degeneracy of the bilayer or icosahedral structures is rooted in the stabilization by p- or d-like cluster orbitals. The importance of low-lying spin states in controlling the electronic and magnetic properties of the cluster is highlighted.     

Non-adiabatic quantum molecular dynamics: basic formalism and case study

A general formalism is presented that treats selfconsistently and simultaneously classical atomic motion and quantum electronic excitations in dynamical processes of atomic many-body systems (non-adiabatic quantum molecular dynamics). On the basis of time-dependent density functional theory, coupled highly non-linear equations of motion are derived for arbitrary basis sets for the time-dependent Kohn-Sham orbitals. Possible approximations to make the approach practical for large atomic cluster systems are discussed. As a first application of the still exact equations of motion, non-adiabatic effects in the scattering of H⁺+H, as a case study, are investigated.     

Magnetic coupling in dinuclear Gd complexes

A spin density functional (SDFT) study of carboxylate-bridged and diazenido-bridged dinuclear gadolinium compounds is presented. Calculated magnetic coupling constants for the carboxylate-bridged structures are in good agreement with experimental data, confirming the ability of the broken symmetry approach used in this work to predict magnetic behavior in such compounds. The systematic trend wherein symmetrically bridged complexes are antiferromagnetically coupled and asymmetrically bridged are ferromagnetically coupled is reproduced by the SDFT calculations. The mechanism underlying magnetic coupling in closed- and open-shell dinuclear complexes is described using a perturbative molecular orbital model that focuses the influence of the 4f(7)-5d exchange interaction on molecular orbitals with significant 5d-orbital character for the complex [[[(Me(3)Si)(2)N](2)(thf)Gd](2)(N(2))]. Open-shell electronic configurations facilitate strong ferromagnetic coupling, whereas in closed-shell systems antiferromagnetic coupling is usually preferred.     

Block-correlated coupled cluster theory: the general formulation and its application to the antiferromagnetic Heisenberg model

The general formalism of the block-correlated coupled cluster (BCCC) method, an alternative multireference coupled cluster method for calculating the ground-state electronic structures of molecular systems, has been presented. The BCCC theory is constructed in terms of a complete set of many-electron states of individual blocks, assumed that the whole system could be partitioned into a set of blocks. The reference state in the BCCC is selected as a tensor product of the most important many-electron state of each system block. By truncating the cluster operator to a certain n-block correlation level, an approximate but size-extensive BCCC method, denoted as BCCCn, is defined. For reducing the computational effort but without much loss of accuracy, the reduced density matrix is introduced to generate an optimal subset of many-electron states for each block. I have implemented the BCCCn (n=2,3) methods within the S=1/2 Heisenberg Hamiltonian, and applied them to calculate the ground-state energies of one-dimensional spin chains and quasi-one-dimensional two-leg spin ladders. The calculated results show that with the appropriate partition of the studied systems the BCCC3 method can yield quite satisfactory ground-state energies for these spin systems.     

Optimization of molecular electronic structure calculations. 2. Calculation of symmetry-reduced matrix elements

A suggested formalism of the local symmetricized orbitals in conjunction with the selection technique for independent blocks of integrals in an original basis is used for a construction of multielectron Hamiltonian matrix elements in the symmetry orbital basis. The optimal molecular electronic structure calculation algorithm with the Hartree–Fock–Roothaan method in the symmetricized basis was obtained as a result. The minimal number of fundamentally distinguished (symmetry attributed) elements both in original and in symmetricized basis is used in the calculations.     

A combined molecular dynamics+quantum mechanics method for investigation of dynamic effects on local surface structures

A combined molecular dynamics (MD)+quantum mechanics (QM) method for studying processes on ionic surfaces is presented. Through the combination of classical MD and ab initio embedded-cluster calculations, this method allows the modeling of surface processes involving both the structural and dynamic features of the substrate, even for large-scale systems. The embedding approach used to link the information from the MD simulation to the cluster calculation is presented, and rigorous tests have been carried out to ensure the feasibility of the method. The electrostatic potential and electron density resulting from our embedded-cluster model have been compared with periodic slab results, and confirm the satisfying quality of our embedding scheme as well as the importance of applying embedding in our combined MD+QM approach. We show that a highly accurate representation of the Madelung potential becomes a prerequisite when the embedded-cluster approach is applied to temperature-distorted surface snapshots from the MD simulation.     

A unified view of the theoretical description of magnetic coupling in molecular chemistry and solid state physics

The magnetic interactions in organic diradicals, dinuclear inorganic complexes and ionic solids are presented from a unified point of view. Effective Hamiltonian theory is revised to show that, for a given system, it permits the definition of a general, unbiased, spin model Hamiltonian. Mapping procedures are described which in most cases permit one to extract the relevant magnetic coupling constants from ab initio calculations of the energies of the pertinent electronic states. Density functional theory calculations within the broken symmetry approach are critically revised showing the contradictions of this procedure when applied to molecules and solids without the guidelines of the appropriate mapping. These concepts are illustrated by describing the application of state-of-the-art methods of electronic structure calculations to a series of representative molecular and solid state systems.     

Importance of structural motifs in liquid hydrogen fluoride

The investigation of liquid phases by means of accurate electronic structure methods is a demanding task due to the high computational effort. We applied second-order M?ller-Plesset perturbation theory and high-level quantum chemical calculations using the coupled-cluster method with single, double and perturbative triple excitations in combination with Dunnings correlation-consistent basis sets up to quintuple ζ quality. Based on these calculations, we extrapolated the correlation energy to the basis set limit in order to improve the results even further. For comparison to the correlated electronic structure methods, density functional calculations employing different functionals are presented as well. The investigated species are a cyclic pentamer as well as a set of branched structures. The quantum cluster equilibrium method is employed for the investigation of the liquid-phase structure of hydrogen fluoride. The pentamer is found to be present to a high extent and in the case of the MP2/QZVP data, its presence improves the results significantly. Accounting for branched structures slightly improves results, so that they are found to be present but not to dominate in liquid hydrogen fluoride. Concerning both the interaction energy and the result of the quantum cluster equilibrium calculation the basis set has a major influence, whereas the difference between M?ller-Plesset perturbation theory and coupled-cluster calculations is less pronounced.     

Ab initio correlation corrections to the Hartree-Fock quasi band-structure of periodic systems employing Wannier-type orbitals

A size-consistent ab initio formalism to calculate correlation corrections to ionization potentials as well as electron affinities of periodic systems is presented. Our approach is based on a Hartree-Fock scheme which directly yields local orbitals without any a posteriori localization step. The use of local orbitals implies non-zero off-diagonal matrix elements of the Fock operator, which are treated as an additional perturbation and give rise to localization diagrams. Based on the obtained local orbitals, an effective Bloch Hamiltonian is constructed to second order of perturbation theory with all third-order localization diagrams included. In addition, the summation of certain classes of diagrams up to infinite order in the off-diagonal Fock elements as well as the Epstein-Nesbet partitioning of the full Hamiltonian are discussed. The problem of intruder states, frequently encountered in many-body perturbation theory, is dealt with by employing the theory of intermediate Hamiltonians. As model systems we have chosen cyclic periodic structures up to an oligoethylene ring in double-zeta basis; however, the theory presented here straightforwardly carries over to infinite periodic systems. Received: 30 April 1998 / Accepted: 27 July 1998 /  Published online: 7 October 1998     

Darwin and mass-velocity relativistic corrections in non-Born-Oppenheimer variational calculations

The Pauli approach to account for the mass-velocity and Darwin relativistic corrections has been applied to the formalism for quantum mechanical molecular calculations that does not assume the Born-Oppenheimer (BO) approximation regarding separability of the electronic and nuclear motions in molecular systems. The corrections are determined using the first order perturbation theory and are derived for the non-BO wave function of a diatomic system expressed in terms of explicitly correlated Gaussian functions with premultipliers in the form of even powers of the internuclear distance. As a numerical example we used calculations of the transition energies for pure vibrational states of the HD(+) ion.     

A machine learning technique toward generating minimum energy structures of small boron clusters

The search for a global minimum related to molecular electronic structure and chemical bonding has received wide attention based on some theoretical calculations at various levels of theory. Particle swarm optimization (PSO) algorithm and modified PSO have been used to predict the energetically stable/metastable states associated with a given chemical composition. Out of a variety of techniques such as genetic algorithm, basin hopping, simulated annealing, PSO, and so on, PSO is considered to be one of the most suitable methods due to its various advantages over others. We use a swarm‐intelligence based parallel code to improve a PSO algorithm in a multidimensional search space augmented by quantum chemical calculations on gas phase structures at 0 K without any symmetry constraint to obtain an optimal solution. Our currently employed code is interfaced with Gaussian software for single point energy calculations. The code developed here is shown to be efficient. Small population size (small cluster) in the multidimensional space is actually good enough to get better results with low computational cost than the typical larger population. But for larger systems also the analysis is possible. One can try with a large number of particles as well. We have also analyzed how arbitrary and random structures and the local minimum energy structures gravitate toward the target global minimum structure. At the same time, we compare our results with that obtained from other evolutionary techniques.     

Electronic structures around the local defects in all-trans-polyacetylene: An analysis by the cluster-series model

A new approach to analyze the electronic structure around the local defects in a polymer chain is developed based on the cluster-series model. In this approach, by extending the cluster molecule to both sides of the defect, the size effect on electronic structure can be estimated systematically and efficiently. Moreover, through the extension process, the periodicity of electronic structure can be extracted in the form of the periodic pattern of stationary orbitals, which are molecular orbitals unaltered by the extension of the cluster. Such periodic orbitals characterize the bulk states of periodic polymer and the energy band structure can be reconstructed from them. Illustrative analyses of some kinds of local defects in all-trans-polyacetylene are presented at the ab initio STO -3G level. The effects of local defects can be detected by the deviation from periodic bulk states. © 1993 John Wiley & Sons, Inc.     

Electronic structure of the [MgO3]+ cation

Accurate ab initio calculations are performed to investigate the stable isomers of [MgO(3)](+) and its lowest electronic states at both molecular and asymptotic regions. The calculations are done using large basis sets and configuration interaction methods including the complete active space self-consistent field, the internally contracted multi-reference configuration interaction, the standard coupled cluster (RCCSD(T)) approaches and the newly implemented explicitly correlated coupled cluster method (RCCSD(T)-F12). The presence of three stable forms is predicted: a cyclic global minimum c-MgO(3)(+), which is followed by a quasi-linear isomer, l2-MgO(3)(+). A third isomer of C(s) symmetry (l1-MgO(3)(+)) is also found. Moreover, we computed the one-dimensional cuts of the six-dimensional potential energy surfaces of the lowest doublet and quartet electronic states of [MgO(3)](+) along the R(MgO) and R(OO) stretching coordinates covering both the molecular and the asymptotic regions. These curves are used later for discussing the metastability of this cation and to propose plausible mechanisms for the Mg(+) + O(3) atmospherically important ion-molecule reaction and related reactive channels.