Multiconfiguration Self-consistent Field Method Research Articles

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).

Multiconfiguration self-consistent-field theory based upon the fragment molecular orbital method

The fragment molecular orbital (FMO) method was combined with the multiconfiguration self-consistent-field (MCSCF) theory. One- and two-layer approaches were developed, the former involving all dimer MCSCF calculations and the latter limiting MCSCF calculations to a small part of the system. The accuracy of the two methods was tested using the six electrons in six orbitals complete active space type of MCSCF and singlet spin state for phenol+(H(2)O)(n), n=16,32,64 (6-31G( *) and 6-311G( *) basis sets); alpha helices and beta strands of phenylalanine-(alanine)(n), n=4,8,16 (6-31G( *)). Both double-zeta and triple-zeta quality basis sets with polarization were found to have very similar accuracy. The error in the correlation energy was at most 0.000 88 a.u., the error in the gradient of the correlation energy was at most 6.x10(-5) a.u./bohr and the error in the correlation correction to the dipole moment was at most 0.018 D. In addition, vertical singlet-triplet electron excitation energies were computed for phenol+(H(2)O)(n), (n=16,32,64), 6-31G( *), and the errors were found to be at most 0.02 eV. Approximately linear scaling was observed for the FMO-based MCSCF methods. As an example, an FMO-based MCSCF calculation with 1262 basis functions took 98 min on one 3.0 GHz Pentium4 node with 1 Gbyte RAM.

Algebraic modifications to second quantization for non-Hermitian complex scaled hamiltonians with application to a quadratically convergent multiconfigurational self-consistent field method

The algebraic structure for creation and annihilation operators defined on orthogonal orbitals is generalized to permit easy development of bound-state techniques involving the use of non-Hermitian Hamiltonians arising from the use of complex-scaling or complex-absorbing potentials in the treatment of electron scattering resonances. These extensions are made possible by an orthogonal transformation of complex biorthogonal orbitals and states as opposed to the customary unitary transformation of real orthogonal orbitals and states and preserve all other formal and numerical simplicities of existing bound-state methods. The ease of application is demonstrated by deriving the modified equations for implementation of a quadratically convergent multiconfigurational self-consistent field (MCSCF) method for complex-scaled Hamiltonians but the generalizations are equally applicable for the extension of other techniques such as single and multireference coupled cluster (CC) and many-body perturbation theory (MBPT) methods for their use in the treatment of resonances. This extends the domain of applicability of MCSCF, CC, MBPT, and methods based on MCSCF states to an accurate treatment of resonances while still using L2 real basis sets. Modification of all other bound-state methods and codes should be similarly straightforward. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Theoretical investigation of the absorption and ionization spectrum of the super greenhouse gas SF5CF3

SF5CF3, recently found in the Earth's atmosphere, is an extremely potent greenhouse gas. Its behaviour under irradiation, as in the upper atmosphere, is of great importance for the possible impact on the global climate. The vertical absorption spectrum of the title compound is studied by various single- and multi-reference ab initio methods and the results are compared to experiments. The best results for valence states are obtained by the multi-state complete active space second order perturbation theory (MS-CASPT2) approach. In contrast, the popular time-dependent density functional theory (TDDFT) gives very poor results. Multi-reference configuration interaction (MRCI) does not yield very accurate energies because only a limited number of valence electrons can be included in the correlation treatment. The Rydberg states are calculated very accurately and efficiently by a frozen-core multi-configuration self-consistent field (FC-MCSCF) method. The accuracy is assessed by quantum defect theory and the experimental and ab initio calculated first ionization potential. The photoelectron spectrum is investigated by the outer-valence Green's functions (OVGF) method. The simulated spectrum is in excellent agreement with a recent experiment.

Calculation of the fine structure and intensity of the singlet–triplet transitions in the imidogen radical

The singlet–triplet transition moments are calculated for the NH radical by multiconfiguration self-consistent field (MCSCF) method with a quadratic response (QR) technique. The band systems in the visible region ( b 1 Σ + → X 3 Σ − and a 1 Δ → X 3 Σ − ) of the NH radical are analyzed in comparison with previous ab initio treatments and with the recent experimental data in attempt to solve some discrepancies. The b 1 Σ + → X 3 Σ Ω − transition moments ratio for the two spin sublevels Ω = 1 and Ω = 0 of the ground state is well reproduced and the radiative lifetime of the b 1 Σ + state ( τ b = 58 ms) is obtained in a good agreement with the experimental value τ b = 53 ( − 13 + 17 ) ms. The A 3 Π ← a 1 Δ transition probability is calculated for the first time and found to be in an excellent agreement with the recent optical pumping measurements of the NH radical in a molecular beam, where population transfer from the metastable a 1 Δ state to the ground X 3 Σ − state is achieved. For the a 1 Δ → X 3 Σ − transition some improvement is achieved in comparison with the previous ab initio results, but the calculated radiative lifetime ( τ a = 3.9 s) is still much lower than the recent measurement provides ( τ a = 12.5 s). The zero field splitting and spin–rotation coupling constants are calculated for the ground state by different methods and advantage of the density functional theory is stressed.

Theoretical study of the electronic states of Nb4, Nb5 clusters and their anions (Nb4-,Nb5-).

Geometries and energy separations of the various low-lying electronic states of Nb(n) and Nb(n) (-) (n=4,5) clusters with various structural arrangements have been investigated. The complete active space multiconfiguration self-consistent field method followed by multireference singles and doubles configuration interaction (MRSDCI) calculations that included up to 52x10(6) configuration spin functions have been used to compute several electronic states of these clusters. The ground states of both Nb(4) ((1)A('), pyramidal) and Nb(4) (-) ((2)B(3g), rhombus) are low-spin states at the MRSDCI level. The ground state of Nb(5) cluster is a doublet with a distorted trigonal bipyramid (DTB) structure. The anionic cluster of Nb(5) has two competitive ground states with singlet and triplet multiplicities (DTB). The low-lying electronic states of these clusters have been found to be distorted due to Jahn-Teller effect. On the basis of the energy separations of our computed electronic states of Nb(4) and Nb(5), we have assigned the observed photoelectron spectrum of Nb(n) (-) (n=4,5) clusters. We have also compared our MRSDCI results with density functional calculations. The electron affinity, ionization potential, dissociation and atomization energies of Nb(4) and Nb(5) have been calculated and the results have been found to be in excellent agreement with the experiment.

Dissociation Potential Curves of Low-Lying States in Transition Metal Hydrides. 2. Hydrides of Groups 3 and 5

The dissociation energy curves of low-lying spin-mixed states for Group 5 hydrides (VH, NbH, and TaH), as well as Group 3 hydrides (ScH, YH, and LaH), have been calculated by using both effective core potential (ECP) and all-electron (AE) approaches. The two approaches are based on the multiconfiguration self-consistent field (MCSCF) method, followed by second-order configuration interaction (SOCI) calculations: the first method employs an ECP basis set proposed by Stevens and co-workers (SBKJC) augmented by a set of polarization functions, and spin−orbit coupling effects are estimated with a one-electron approximation, using effective nuclear charges. The second method employs a double-ζ basis set developed by Huzinaga (MIDI) and three sets of p functions are added to both transition element and hydrogen and one set of f functions is also added to the transition element. The relativistic elimination of small components (RESC) scheme and full Breit−Pauli Hamiltonian are employed in the AE approaches to incorporate relativistic effects. 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 the hydrides, filling a considerable gap in available data for these molecules. Transition moments are also computed among the spin-mixed states, and qualitative agreement is obtained for Group 3 hydrides in comparison with the experimental results reported by Ram and Bernath. Peak positions of emission spectra in Group 5 hydrides are also predicted.

Electronic states for Al 2As 2 and its ions

Low-lying electronic states of Al 2As 2 and its ions are investigated using the complete active space multiconfiguration self-consistent field(CASSCF) method and the density functional theory (DFT:B3LYP). The vibrational frequencies and IR intensities of the electronic states are calculated and presented at the DFT level, which conforms that these states have stable minima at their geometry structures. Results suggest the rhombus structure is the equilibrium geometry for the ground states and most excited states of Al 2As 2 and its ions. The adiabatic ionization potential and other properties of Al 2As 2 are predicted and discussed.

Theoretical study of the electronic states of niobium trimer (Nb3) and its anion (Nb3−)

Geometries and energy separations of the various low-lying electronic states of niobium trimer (Nb3) and its anion (Nb3−) with triangular and linear structural arrangements have been investigated. The complete active space multiconfiguration self-consistent field method followed by multireference singles plus doubles configuration interaction (MRSDCI) that included up to 48 million configuration spin functions have been used to compute several electronic states of these clusters. The geometries of ground and excited states of Nb3 and Nb3− are triangular. The ground states of both Nb3 (2B1) and Nb3− (1A1) have been found to be of low spin. The low-lying electronic states with degenerate symmetries in the D3h group are distorted to the C2v structure (from the ideal D3h) due to the Jahn–Teller effect. On the basis of the energy separations of our computed electronic states of Nb3, we have assigned the observed photoelectron spectrum of Nb3−. We have also compared our MRSDCI results with density functional calculations. The electron affinity, ionization potential, dissociation and atomization energies of Nb3 have been calculated and the results have been found to be in excellent agreement with the experiment.

Ab initio modelling of transition metals in diamond

Transition metals (TM) from the first transition series are commonly used as solventcatalysts in the synthesis of diamond by high pressure, high temperature processes. Abinitio calculations on these metals, in finite clusters of tetrahedrally coordinated carbon,enable us to investigate trends in their stability and properties. By carrying out systematicstudies of interstitial, substitutional and semi-vacancy TM defects, we show thatthe electronic structure of the TMs is complicated by the presence of ‘danglingbonds’ when the TM disrupts the crystal lattice: interstitial defects conform to theLudwig–Woodbury (LW) model, whilst substitutional and semi-vacancy defects movefrom approximating the LW model early in the transition series to approachingthe vacancy model for the heavier metals. Multi-configurational self-consistentfield methods allow genuine many-electron states to be modelled; for neutralinterstitial, and all substitutional TMs, the crystal fields are found to exceed theexchange energies in strength. Consequently, low spin states are found for thesedefects. We find substitutional defects to be the most stable, but that semi-vacancyTMs are very similar in energy to the substitutional defects late in the transitionseries; interstitial defects are only metastable in diamond. Given appropriatecharge compensators neutral and positively charged interstitial TM defects werestable, while negatively charged species appeared to be strongly disfavoured.

Theoretical study of the structure of propanal in the first excited singlet and triplet electronic states: three-dimensional model for torsional and inversion vibrations

Potential energy surfaces of the conformationally nonrigid propanal molecule (CH 3CH 2CHO) in the lowest excited triplet (T 1) and singlet (S 1) electronic states were calculated by the multiconfigurational self-consistent field method CASSCF. Electronic excitations of the propanal conformers from the ground state (S 0) to the excited states (T 1 and S 1) were demonstrated to cause essential changes in the molecular structure, viz. the rotation of the ethyl tops and the out-of-plane distortion of carbonyl fragments. Nuclear vibrational motions in the propanal molecule in the excited electronic states were analyzed both in the harmonic approximation and by the use of the one-, two-, and three-dimensional variational calculations to describe correlated large-amplitude vibrations.

A MCSCF method for ground and excited states based on full optimizations of successive Jacobi rotations.

A new multiconfigurational self-consistent field (MCSCF) method based on successive optimizations of Jacobi rotation angles is presented. For given one- and two-particle density matrices and an initial set of corresponding integrals, a technique is developed for the determination of a Jacobi angle for the mixing of two orbitals, such that the exact energy, written as a function of the angle, is fully minimized. Determination of the energy-minimizing orbitals for given density matrices is accomplished by successive optimization and updating of Jacobi angles and integrals. The total MCSCF energy is minimized by alternating between CI and orbital optimization steps. Efficiency is realized by optimizing CI and orbital vectors quasi-simultaneously by not fully optimizing each in each improvement step. On the basis of the Jacobi-rotation based approach, a novel MCSCF procedure is formulated for excited states, which avoids certain shortcomings of traditional excited-state MCSCF methods. Applications to specific systems show the practicability of the developed methods.

On the infinitude of non–zero eigenvalues of the single–electron density matrix for atoms and molecules

It is demonstrated that the exact electronic ground–state wave function for any atom or molecule has a single–electron density matrix with infinitely many non–zero eigenvalues. Ensuing theoretical considerations on standard approximate methods in quantum chemistry (the configuration–interaction and multi–configuration selfconsistent field methods) are presented.

Modeling of Biomolecular Systems with the Quantum Mechanical and Molecular Mechanical Method Based on the Effective Fragment Potential Technique: Proposal of Flexible Fragments

Development and applications of a new approach to hybrid quantum mechanical and molecular mechanical (QM/MM) theory based on the effective fragment potential (EFP) technique for modeling properties and reactivity of large molecular systems of biochemical significance are described. It is shown that a restriction of frozen internal coordinates of effective fragments in the original formulation of the theory (Gordon, M. S.; Freitag, M. A.; Bandyopadhyay, P.; Jensen, J. H.; Kairys, V.; Stevens, W. J. J. Phys. Chem. A 2001, 105, 293) can be removed by introducing a set of small EFs and replacing the EFP−EFP interactions by the customary MM force fields. The concept of effective fragments is also utilized to solve the QM/MM boundary problem across covalent bonds. The buffer fragment, which is common for both subsystems, is introduced and treated specially when energy and energy gradients are computed. An analysis of conformations of dipeptide−water complexes, as well as of dipepties with His and Lys residues, confirms the reliability of the theory. By using the Hartree−Fock and MP2 quantum chemistry methods with the OPLS-AA molecular mechanical force fields, we calculated the energy difference between the enzyme−substrate complex and the first tetrahedral intermediate for the model active site of the serine protease catalytic system. In another example, the multiconfigurational complete active space self-consistent field (CASSCF) method was used to model the homolytic dissociation of the peptide helix over the central C−N bonds. Finally, the potentials of internal rotation of the water dimer considered as a part of the water wire inside a polyglycine analogue of the ion channel gramicidin A were computed. In all cases, an importance of the peptide environment from MM subsystems on the computed properties of the quantum parts is demonstrated.

Deuterium NMR and Ab Initio Studies of Strongly Hydrogen-Bonded Molecules

Two newly synthesized alkylated cyanomalonaldehyde derivatives possess very short intramolecular hydrogen bonds, which are studied by deuterium NMR. Both the dimethyl and di- tert-butyl derivatives have small deuterium quadrupole coupling constants and large asymmetry parameters. In addition, the di- tert-butyl compound, which has one of the shortest O– D…O hydrogen bonds yet measured, has a quadrupole coupling which anomalously increases with temperature. The significance of these phenomena is explored using a theoretical model which employs vibrationally averaged ab initio electric field gradient tensors calculated with large basis sets and electron correlation via the multiconfigurational self-consistent field method.

Spin–spin coupling constants in ethylene: equilibrium values

The nuclear magnetic resonance spin–spin coupling constants for the ethylene have been calculated at the multiconfigurational self-consistent field (MCSCF) method using the restricted (RAS) and complete (CAS) active space approximations. An analysis of the calculated values and of the effects of different factors (active spaces, valence and core–electron correlation) is presented. The effect of increase the number of active orbitals and that of triple and quadruple excitations is important and opposite to the effect of core–electron correlation. The best calculated values for 1J CC (68.83 Hz), 1J CH (151.56), 2J CH (−1.56 Hz), 2J HH (1.07 Hz) 3J HH (cis) (11.47 Hz), and 3J HH (trans) (17.78 Hz) are in good agreement with the best calculated and experimental values.

Cubic nonlinear optical response of a molecule in an inhomogeneous solvation environment: A response theory formalism

A method for determining cubic response molecular properties of heterogeneously solvated molecules is presented. The molecule is either located at the surface of a metal or solvated alongside the surface of a metal. We represent the metal as a perfect conductor and the solvent as a dielectric medium. The electronic structure of the molecular systems is described both at the uncorrelated and correlated electronic structure levels. The latter is given by the multiconfigurational self-consistent field method. From this method it is possible to calculate fourth order molecular properties such as frequency-dependent second-order hyperpolarizabilities (γ), three-photon absorptions, two-photon absorption between excited states, and frequency-dependent polarizabilities of excited states. From the frequency-dependent second-order hyperpolarizabilities one can calculate for heterogeneously solvated molecules the third harmonic generation, the static electric field-induced second harmonic generation, the static electric field induced Kerr effect. Calculations of the frequency dependent second-order hyperpolarizability tensor for heterogeneously solvated CO are presented. The calculations show that the second-order hyperpolarizability tensor elements depend strongly on the heterogeneous solvent configuration.

Spectroscopic properties of lead hexamer and its ions (Pb6, Pb6+, Pb6−)

We have computed the optimized geometries and energy separations of low-lying electronic states of the lead hexamer (Pb6) and its positive and negative ions. Our techniques have included high level relativistic electron correlation techniques such as complete active space multiconfiguration self-consistent field (CAS-MCSCF) method followed by large scale multireference singles plus doubles configuration interaction (MRSDCI) and relativistic configuration interaction (RCI) computations that included up to 16 million configurations. Our computed results have facilitated the assignment of the anion photodetachment spectra of Pb6− and also in the prediction of the properties of yet to be observed electronic states. A 1A1g tetragonal bipyramid structure (D4h symmetry) is found as the ground state for Pb6. The excitation energy, atomization energies, ionization potentials, and vertical and adiabatic electron affinities are computed and compared with the experimental results. We have assigned the observed X, A, B, C, D, and E states of the anion photoelectron spectra of Pb6−, and discuss spin–orbit versus Jahn-Teller effects.

Dissociation Potential Curves of Low-Lying States in Transition Metal Hydrides. I. Hydrides of Group 4

The dissociation energy curves of low-lying spin-mixed states for Group 4 hydrides, TiH, ZrH, and HfH, have been calculated using both effective core potential and all-electron approaches. A comprehensive set of theoretical results including the dissociation energies, equilibrium distances, harmonic frequencies, anharmonicities, rotational constants, and dipole moments are reported for these molecules. We present results for both ground and a few excited states, filling a considerable gap in available data for these molecules. Absorption spectra are also predicted on the basis of the results. The present study uses three methods, all based on the multiconfigurational self-consistent field (MCSCF) method, augmented by second-order configuration interaction (SOCI), with either an effective core potential basis set (SBKJC) or a double-ζ basis set (MIDI): (i) MCSCF+SOCI/SBKJC(f,p) with a one-electron approximation using effective nuclear charges, (ii) MCSCF+SOCI/MIDI(3p,3p) with the full Breit−Pauli Hamiltonian, and (iii) MCSCF +SOCI/MIDI(3p,3p) with the relativistic elimination of the small component scheme and full Breit−Pauli Hamiltonian. The results are compared with previous theoretical studies and available experimental data reported previously. Good agreement is obtained between the results obtained when the first and third methods are used.

Nonempirical Quantum-Chemical Calculations of the Structure and Conformations of the 2,2-Dichloroethanal Molecule in the Lowest Excited Singlet State

The structure of the 2,2-dichloroethanal molecule (CHCl2CHO) in the lowest excited singlet state was calculated by the nonempirical multiconfigurational self-consistent field method. The electron transition of CHCl2CHO from the ground to lowest excited singlet state is accompanied by rotation of the CHC12 group, and the carbonyl fragment becomes nonplanar. The potential energy surface for the excited CHCl2CHO molecule contains six minima corresponding to three pairs of enantiomers. This surface was used to solve torsion and inversion motion problems in the one-dimensional approximation and also two-dimensional torsion-inversion problem. Comparison of the results showed a relation between torsion and inversion motions.