Multiconfiguration Self-consistent Field Method Research Articles

Spectra and oscillator strengths of 3p63d9–3p53d10 and 3p63d9–3p63d84p transitions for cobalt-like Sn23+ ion

This paper calculates the spectra and oscillator strengths for highly ionized cobalt-like Sn23+ ions 3p63d9–3p53d10, 3p63d9–3p63d84p transitions by using a multi-configuration self-consistent field method program together with the proposed fitting formula. The calculations have a good agreement with observations.

Pure organic magnetic polymer and an ab initio SCF-MO calculation

An ab initio SCF-MO calculation was performed on dibenzo [cd.lm] dicyclopenta [ghi.pqr] perylene using UHF/DFT/BP86 geometry. The modified perylene compound has two degenerate highest occupied molecular orbitals (HOMOs) with single electron each at −9.605 and −9.504 eV calculated by multi-configuration self-consistent field (MCSCF) method and it is a stable triplet ground state. A ladder polymer was designed with dibenzo [cd.lm] dicyclopenta [ghi.pqr] perylene such that two different polycyclic conjugated modules were connected alternatively to the ladder chain. The basic unit of the polymer was optimized to UHF/DFT/BP86 geometry and eigen values were calculated. Each ring in the ladder polymer chain is a 4 n cyclic pi system with peripheral electrons and has a triplet ground state. Finally, NICS, EPR and ZFS spectra were calculated for the dibenzo [cd.lm] dicyclopenta [ghi.pqr] perylene and the basic unit of polymer using DFT methods. It is observed that each polymer molecule is like a single-molecule magnet (SMM) – an object that is composed of molecules each of which behaves as an individual paramagnet.

Investigation of 2P Be− Shape Resonances Using a Quadratically Convergent Complex Multiconfigurational Self-Consistent Field Method

We develop, implement, and apply a quadratically convergent complex multiconfigurational self-consistent field method (CMCSCF) that uses the complex scaling theorem of Aguilar, Balslev, and Combes within the framework of the multiconfigurational self-consistent field method (MCSCF) in order to theoretically investigate the resonances originated due to scattering of a low-energy electron off of a neutral or an ionic target (atomic or molecular). The need to scale the electronic coordinates of the Hamiltonian as prescribed in the complex scaling theorem requires the use of a modified second quantization algebra suitable for biorthonormal spin orbital bases. In order to control the convergence to a stationary point in the complex energy hypersurface, a modified step-length control algorithm is incorporated. The position and width of 2P Be- shape resonances are calculated by inspecting the continuum states of Be-. To our knowledge, this is the first time that CMCSCF has been directly used to determine electron-atom/molecule scattering resonances. We demonstrate that both relaxation and nondynamical correlation are important for accurately describing shape resonances. For all of the calculations, the quadratically convergent CMCSCF was found to converge to the correct stationary point with a tolerance of 1.0 x 10(-10) au for the energy gradient within 10 iterations or less.

Accurate ab initio density fitting for multiconfigurational self-consistent field methods

Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field (CASSCF) method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra-mu-acetato-dicopper(II), and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxiliary basis sets constructed from Cholesky decomposition of the atomic electron repulsion integrals.

Multiconfiguration optimized effective potential method for a density-functional treatment of static correlation

An approach to treat static correlation within a density-functional framework is presented. To that end, a multiconfiguration optimized effective potential (MCOEP) method is derived. In contrast to standard multiconfiguration self-consistent field (MCSCF) methods and previous combinations of MCSCF procedures with density-functional theory, the MCOEP method yields well-defined physically meaningful orbital and eigenvalue spectra. In addition to the electronic ground state also excited electronic states can be described. The MCOEP method is implemented invoking the localized Hartree-Fock approximation, leading to a multiconfiguration localized Hartree-Fock approach. Applications of the new method to the dissociation of the hydrogen molecule and the isomerization of ethene and cyclobutadiene show that it is capable of describing situations that are characterized by strong static correlation.

Potential energy curve for isomerization of N2H2 and C2H4 using the improved virtual orbital multireference Møller–Plesset perturbation theory

Multireference Møller-Plesset (MRMP) perturbation theory [K. Hirao, Chem. Phys. Lett. 190, 374 (1992)] is modified to use improved virtual orbitals (IVOs) and is applied to study ground state potential energy curves for isomerization and dissociation of the N2H2 and C2H4 molecules. In contrast to traditional MRMP or multistate multiconfiguration quasidegenerate perturbation theory where the reference functions are obtained from (often difficult to converge) state averaged multiconfiguration self-consistent field methods, our reference functions are represented in terms of computationally efficient IVOs. For convenience in comparisons with other methods, a first order complete active space configuration interaction (CASCI) calculation with the IVOs is followed by the use of the IVOs in MRMP to incorporate residual electron correlation effects. The potential energy curves calculated from the IVO-MRMP method are compared with computations using state-of-the-art coupled cluster singles and doubles (CCSD) methods and variants thereof to assess the efficacy of the IVO-MRMP scheme. The present study clearly demonstrates that unlike the CCSD and its variants, the IVO-MRMP approach provides smooth and reliable ground state potential energy curves for isomerization of these systems. Although the rigorously size-extensive completely renormalized CC theory with noniterative triples corrections (CR-CC(2,3)) likewise provides relatively smooth curves, the CR-CC(2,3) calculations overestimate the cis-trans barrier height for N2H2. The ground state spectroscopic constants predicted by the IVO-CASCI method agree well with experiment and with other highly correlated ab initio methods.

On the electronic structure of small cyclic carbon clusters

We present the results of correlated calculations on a variety of small carbon rings. Equilibrium structures and vibrational frequencies are calculated and transition states connecting symmetry-equivalent minima are considered in detail. We show that neither single-reference coupled-cluster nor multiconfigurational self-consistent field methods (even after perturbational inclusion of dynamical correlation effects) give qualitatively correct potential surfaces in the vicinity of the minima, suggesting that there is little recourse for these systems other than a multireference coupled-cluster treatment. Density-functional theory using the B3LYP functional produces results broadly in agreement with single-reference coupled-cluster methods and is thus no more reliable, but considerably more economical.

Approximating correlation effects in multiconfigurational self-consistent field calculations of spin-spin coupling constants

The multiconfigurational self-consistent field (MCSCF) method in their approximations restricted and complete active spaces (RAS and CAS) provides a theoretically accurate description of the coupling constants of a wide range of molecules. To obtain accurate results, however, very large basis sets and large configuration spaces must be used. Nuclear magnetic resonance coupling constants for the equilibrium geometry have been calculated for a series of small molecules using approximated correlation contributions. The four contributions to the coupling constants (Fermi contact, spin dipolar, orbital paramagnetic, and orbital diamagnetic) have been calculated at the CAS and RAS MCSCF and second-order polarization propagator approximation levels using a large basis set. An additive model that considers the effect on the coupling constants from excitation of more than two electrons and from core-electron correlation is used to estimate the coupling constants. Compared with the experimental couplings, the best calculated values, which correspond to the MCSCF results, present a mean absolute error of 3.6 Hz and a maximum absolute deviation of 13.4 Hz. A detailed analysis of the different contributions and of the effects of the additive contributions on the coupling constants is carried out.

Ab initio calculation of C—I bond dissociation of two alkyl iodide molecules

Employing the multiconfiguration self-consistent field method and the multiconfiguration quasi-degenerate perturbation method, the adiabatic potential energy curves and vertical excitation energies of alkyl iodides CF3I and C2H2F3I are calculated for the low-lying states， respectively. It is found that the low-lying excited states of the two molecules are repulsive, and the calculated dissociation energies for their ground states are 2.473eV and 2.835eV, respectively, in which the former one agrees well with the experimental results.

Equivalent orbitals for multiconfigurational spin‐tensor electron propagator method (MCSTEP): The vertical ionization potentials of B, NO, CF, and OF

AbstractThe multiconfigurational spin tensor electron propagator method (MCSTEP) was developed as an implementation of electron propagator/single particle Green's function methods for ionization potentials (IPs) and electron affinities (EAs). MCSTEP was specifically designed for open shell and highly correlated (nondynamically correlated) initial states. For computational efficiency the initial state used in MCSTEP is typically a small complete active space (CAS) multiconfigurational self‐consistent field (MCSCF) state. If in a molecule there are some degenerate orbitals which are not fully or half occupied, usual MCSCF calculations will make these orbitals inequivalent, i.e., the occupied ones will be different from the nonoccupied ones, so that the degeneracy is broken. In this article, we use a state averaged MCSCF method to get equivalent orbitals for the initial state and import the integrals into the subsequent MCSTEP calculations. This gives, in general, more reliable MCSTEP vertical IPs. © 2008 Wiley Periodicals, Inc., 2008

Multireference self-consistent-field energies without the many-electron wave function through a variational low-rank two-electron reduced-density-matrix method

The variational two-electron reduced-density-matrix (2-RDM) method allows for the computation of accurate ground-state energies and 2-RDMs of atoms and molecules without the explicit construction of an N-electron wave function. While previous work on variational 2-RDM theory has focused on calculating full configuration-interaction energies, this work presents the first application toward approximating multiconfiguration self-consistent-field (MCSCF) energies via low-rank restrictions on the 1- and 2-RDMs. The 2-RDM method with two- or three-particle N-representability conditions reduces the exponential active-space scaling of MCSCF methods to a polynomial scaling. Because the first-order algorithm [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] represents each form of the 1- and 2-RDMs by a matrix factorization, the RDMs are readily defined to have a low rank rather than a full rank by setting the matrix factors to be rectangular rather than square. Results for the potential energy surfaces of hydrogen fluoride, water, and the nitrogen molecule show that the low-rank 2-RDM method yields accurate approximations to the MCSCF energies. We also compute the energies along the symmetric stretch of a 20-atom hydrogen chain where traditional MCSCF calculations, requiring more than 17x10(9) determinants in the active space, could not be performed.

Structure and stability of various states of the EuC and EuC 2 molecules

B3LYP level density functional theory (DFT) and multiconfiguration self-consistent-field (MCSCF) level ab initio method calculations have been performed on the basis of relativistic effective core potentials to investigate the nature of EuC and EuC2 molecules. The computed results indicate that the ground states of EuC and EuC2 are 12∑+ and 8A2, respectively. Dissociation potential energy curves of the low-lying electronic states of EuC have been calculated using the MCSCF method, and the same level calculation on EuC2 indicates that the dissociation energy of EuC2 of ground state compares well with the available experimental data. The bond characteristic is also discussed using Mulliken populations.

Theoretical Study of Structure, Vibrational Frequencies, and Electronic Spectra of Dibenzofuran and Its Polychlorinated Derivatives

Minimum structures and harmonic vibrational frequencies of dibenzofuran (DF), 2,3,7,8-tetrachlorodibenzofuran (TCDF), and octachlorodibenzofuran (OCDF) were calculated using the multiconfigurational complete active space self-consistent field (CASSCF) and density functional theory (DFT) methods. The electronic transitions in these compounds were studied via the single-state multireference second-order perturbation theory (CASPT2) based on the CASSCF(14,13) references, as well as the time-dependent DFT (TD-B3P86) employing the cc-pVDZ (CASSCF/CASPT2) and 6-31G(d,p) (TD-B3P86) basis sets. The B3P86 geometry and harmonic vibrational frequencies of ground state DF agree very well with the experimental data, and the CASSCF/CASPT2 excitation energies and oscillator strengths are accurate enough to provide a reliable assignment of the absorption bands in the 200-300 nm region. The close agreements with experiment for the parent DF give the present theoretical approaches a valuable credit in predicting the properties of the environmentally toxic polychlorinated congeners, which is all the more important considering the difficulties and hazards in obtaining the experimental data.

Virtual synthesis of artificial molecules of In, Ga, and As with predesigned electronic properties using a self-consistent field method

A Hartree-Fock based (HF), multiconfiguration self-consistent field (MCSCF) method has been used to configure computationally several nonstoichiometric model pyramidal molecules of In, Ga, and As atoms with a predesigned electronic energy level structure. The geometry, structure, and composition of the molecules have been derived from those of the corresponding bulk lattices. Formation of the molecules under conditions mimicking vacuum and quantum confinement has been studied. The results prove that formation conditions affect the molecular parameters (such as the structure and bond length), thus causing significant effects (up to an order of magnitude) on the electronic properties of the molecules, including their charge and spin density distributions (CDDs and SDDs, respectively). The virtual (i.e., fundamental theory based, computational) synthesis of atomic-scale objects with predesigned physicochemical properties is a powerful method that can be used to develop electronic templates of artificial molecules, atomic clusters, small quantum dots (QDs), QD-based nanoheterostructures (NHSs), and other nanosystems of practical interest to guide their experimental realization.

CORRELATED ELECTRONIC STRUCTURE NONLINEAR RESPONSE METHODS FOR STRUCTURED ENVIRONMENTS

This contribution concerns a brief outline of structural environment models where correlated electronic structure response methods are utilized for the determination of nonlinear optical properties of molecules. The presentation provides theory and applications of a heterogeneous dielectric media model and a quantum mechanical-classical mechanical model at the level of correlated electronic structure response methods. The correlated electronic structure response methods include the multiconfigurational self-consistent field method.

Ab initiocalculations of external-field shifts of the661−nmquadrupolar clock transition in neutral Ag atoms

Frequency shifts of the Ag I 4d105s 2S1/2(F=0,MF=0) to 4d95s2 2D5/2(F[prime]=2,MF[prime]=0) electric-quadrupole transition at 330.6 nm due to external fields are calculated using multiconfigurational self-consistent field methods. As this forbidden transition is free from first order Doppler and Zeeman effects, it is under investigation for the realization of an atomic optical clock. The calculated perturbations are the light shift, the blackbody frequency shift, and the quadratic Zeeman shift. Results show that a total uncertainty of 10–18 could be reach without confining the atoms in a Lamb-Dicke regime in an optical lattice.

Dissociation Potential Curves of Low-Lying States in Transition Metal Hydrides. 3. Hydrides of Groups 6 and 7

The dissociation curves of low-lying spin-mixed states in monohydrides of groups 6 and 7 were calculated by using an effective core potential (ECP) approach. This approach is based on the multiconfiguration self-consistent field (MCSCF) method, followed by first-order configuration interaction (FOCI) calculations, in which the method employs an ECP basis set proposed by Stevens and co-workers (SBKJC) augmented by a set of polarization functions. Spin-orbit coupling (SOC) effects are estimated within the one-electron approximation by using effective nuclear charges, since SOC splittings obtained with the full Breit-Pauli Hamitonian are underestimated when ECP basis sets are used. The ground states of group 6 hydrides have Omega = (1)/(2)(X(6)Sigma(+)(1/2)), where Omega is the z component of the total angular momentum quantum number. Although the ground states of group 7 hydrides have Omega = 0(+), their main adiabatic components are different; the ground state in MnH originates from the lowest (7)Sigma(+), while in TcH and ReH the main component of the ground state is the lowest (5)Sigma(+). The present paper reports a comprehensive set of theoretical results including the dissociation energies, equilibrium distances, electronic transition energies, harmonic frequencies, anharmonicities, and rotational constants for several low-lying spin-mixed states in these hydrides. Transition dipole moments were also computed among the spin-mixed states and large peak positions of electronic transitions are suggested theoretically for these hydrides. The periodic trends of physical properties of metal hydrides are discussed, based on the results reported in this and other recent studies.

Electronic Properties and Stability of Artificial In-N Molecules

ABSTRACTIn the work reported here the Hartree-Fock (HF), restricted open shell HF (ROHF), and multiconfiguration self-consistent field (CI/CASSCF/MCSCF) methods are used to predict electronic properties of several artificial molecules of InAsN and indium nitride whose structure and composition have been derived from those of the corresponding symmetry elements of the zincblende and wurtzite bulk lattices. Both quantum-confined and “vacuum” clusters (whose geometry has been optimized without any spatial constraints applied to the atomic positions) were studied focusing on the electronic energy level structure, direct optical transition energy (OTE), and charge and spin distributions. The obtained results indicate that inclusion of “impurity” atoms (such as As atoms) may enhance stability of both vacuum and confined pyramidal In-N molecules and provide for manipulations of the OTE in a wide range of its values. The CI/CASSCF/MCSCF OTEs of the studied wurtzite-based clusters may also vary in a wide range, from 1.7440 eV for the smallest pre-designed prismatic molecule In6N6 to 6.9780 eV for its almost perfect prismatic “vacuum” counterpart. These evaluations closely correlate with experimental data available in literature.

Virtual Synthesis and Optoelectronic Properties of Prismatic Artificial Molecules of In-N and Zn-O: Comparative Studies

ABSTRACTThe Hartree-Fock (HF), restricted open shell HF (ROHF), configuration interaction (CI), complete active space (ICASCF), and multiconfiguration self-consistent field (MCSCF) methods provide sophisticated fundamental theory-based, computational tools to study structure, composition,chemistry and electronic properties of small artificial molecules composed of semiconductor compound atoms. These tools are used to synthesize virtually several prismatic In-N and Zn-O artificial molecules whose structure is derived from that of the symmetry elements of the respective wurtzite bulk lattices. Applications of spatial constraints to the atomic coordinates allow modeling molecular synthesis in quantum confinement, to obtain pre-designed molecules with tunable electronic properties. Relaxation of these constraints, or optimization, leads to the corresponding molecules synthesized in “vacuum”. The development of computational templates of the studied artificial molecules synthesized in confinement reflects effects of quantum confinement on the electronic level structure, bonding, the direct optical transition energy, and charge and spin density distributions of the molecules. Comparison of the structure and properties of these molecules to those of their vacuum counterparts leads to a conclusion that a small changes in atomic positions in otherwise structurally similar molecules cause a significant change in their electronic properties. Thus, the electronic properties of artificial molecules can be tuned by changing their synthesis conditions that are defined by atomistic details of quantum confinement where the molecules are synthesized.

Calculation of properties of the ozone molecule by the multiconfigurational self-consistent field method

For the ground state of the ozone molecule, by using the multiconfigurational self-consistent field method, we calculated the electric and magnetic properties — quadrupole moment, polarizability, tensor of magnetic susceptibility, nuclear quadrupole interaction constant, and the rotational g-factor. Qualitative agreement between the calculated parameters and experimental values was obtained. The tensors of chemical shielding in the spectrum of the nuclear magnetic resonance for the 17O isotopes have also been predicted (without allowance for the contribution made by the spin of the electrons).