Effective dynamic correlation in multiconfigurational wave-function calculations on atoms and molecules

An intuitive understanding of dynamic correlation in terms of a regularized electron repulsion expression is outlined. Expressions for cusp kinetic energy corrected regularized electron repulsion integrals are deduced and implemented in a multiconfigurational wave-function framework. A regularized complete active space self-consistent field (reg-CASSCF) technique is suggested and tested on atomic total energies, molecular structures and binding energies. Received: 26 November 1996 / Accepted: 21 April 1997     

A simplified method for molecular correlation energy calculations by separation into internal and non-internal parts. Application to multiconfigurational zeroth-order wavefunctions

A simplified method of determining the molecular correlation energy by two separate calculations, one for the internal and one for the non-internal correlation energies, is extended to multiconfigurational zeroth-order wavefunctions. This extension offers the possibility of deriving correlated potential energy curves or surfaces for processes involving configurational changes. The internal correlation energy is shown to be correctly determined by an MC/CI procedure combining the use of minimal and extended basis sets. An original semi-empirical “atoms-in-molecules” method based on the L.C.A.O. expansion of the molecular wavefunction is proposed for the non-internal correlation energy calculations. This method is shown to be able to overcome some of the shortcomings of a previous populations analysis approach. Test calculations concern potential curve parameters (D _e ,T _e ,R _e ,W _e ) of the ground and some excited states of the NH, C₂, HCN and CN molecules. The results are found to be in good agreement with corresponding experimental and large CI results. Aspirant du Fonds National Belge de la Recherche Scientifique Boursier I.R.S.I.A.     

Path integral based calculations of symmetrized time correlation functions. II

Schofield's form of quantum time correlation functions is used as the starting point to derive a computable expression for these quantities. The time composition property of the propagators in complex time is exploited to approximate Schofield's function in terms of a sequence of short time classical propagations interspersed with path integrals that, combined, represent the thermal density of the system. The approximation amounts to linearization of the real time propagators and it becomes exact with increasing number of propagation legs. Within this scheme, the correlation function is interpreted as an expectation value over a probability density defined on the thermal and real path space and calculated by a Monte Carlo algorithm. The performance of the algorithm is tested on a set of benchmark problems. Although the numerical effort required is considerable, we show that the algorithm converges systematically to the exact answer with increasing number of iterations and that it is stable for times longer than those accessible via a brute force, path integral based, calculation of the correlation function. Scaling of the algorithm with dimensionality is also examined and, when the method is combined with commonly used filtering schemes, found to be comparable to that of alternative semiclassical methods.     

Atranes. II. Dipole moments and structure of silatranes

Possible steric configurations of 1-organyl- and 1-organoxysilatranes,, are considered. The dipole moments of six compounds of this type (X=CH₃, (CH₃)₂CH, CH₂=CH, C₆H₅, C₂H₅O, C₆H₅O) have been found experimentally to be extremely high, 5.3–7.1 D. They conclusively show that the silatranes contain a semipolar transannular coordinate bond SiN between the negatively charged 5 -covalent silicon atom in the middle of the planar SiO₃ group and the tetrahederal onium nitrogen atom.Part I, see [1].     

State correlation diagrams for the photochemical reactions of organometallics

State correlation diagrams are proposed for a number of photochemical reactions of organometallics. Spin-orbit coupling is found important to understand the reactivity of these organometallics.     

Determination of molecular properties by the method of moments. II

The wave functions and energies of a number of diatomic molecules have been determined for different nuclear separations by both the method of energy variation and the method of moments. The results obtained by the two methods are compared and indicate definite advantages of the method of moments over the method of energy variation.

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Zusammenfassung Für eine Reihe zweiatomiger Moleküle werden für verschiedene Kernabstände die Wellenfunktionen und Energien nach der Methode der Energievariation und nach der neueren Momentenmethode bestimmt. Der Vergleich der Ergebnisse zeigt, daß die Momentenmethode erhebliche Vorteile besitzt gegenüber der üblichen Methode der Energievariation.

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Résumé Les fonctions d'onde et les énergies de plusieurs molécules diatomiques ont été déterminées à différentes distances internucléaires par la méthode de variation de l'énergie et par la méthode des moments. Les résultats comparés des deux méthodes indiquent de nets avantages de la méthode des moments sur la méthode de variation de l'énergie.

     

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. II. Coulomb interaction effects in single conjugated polymer chains

Conjugated polymers have attracted considerable attention in the last few decades due to their potential for optoelectronic applications. A key step that needs optimisation is charge carrier separation following photoexcitation. To understand better the dynamics of the exciton prior to charge separation, we have performed simulations of the formation and dynamics of localised excitations in single conjugated polymer strands. We use a nonadiabatic molecular dynamics method which allows for the coupled evolution of the nuclear degrees of freedom and of multiconfigurational electronic wavefunctions. We show the relaxation of electron-hole pairs to form excitons and oppositely charged polaron pairs and discuss the modifications to the relaxation process predicted by the inclusion of the Coulomb interaction between the carriers. The issue of charge photogeneration in conjugated polymers in dilute solution is also addressed.     

Second-row molecular orbital calculations: II. Semi-empirical calculations of dipole moments

The ability of four semi-empirical methods to predict dipole moments of molecules containing atoms in the second row of the periodic table is investigated. None of the methods is capable of consistently reproducing either magnitudes or qualitative trends; however, the CNDO method of Santry gives the best agreement overall. The original CNDO method of Santry and Segal emphasizes the importance of d orbitals to a greater extent than does the Santry method. Comparisons are presented with non-empirical results when possible.     

The electrostatic potential generated by topological atoms. II. Inverse multipole moments

Quantum chemical topology defines finite atoms, whose bounded electron density generates a well-defined electrostatic potential. A multipole expansion based on spherical tensors provides a potential that is formally convergent outside the divergence sphere. Part I of this series [P. L. A. Popelier and M. Rafat, Chem. Phys. Lett.376, 148 (2003)] showed that a continuous multipole expansion expands the convergence region, thereby allowing the electrostatic potential to be evaluated at short range. Here, we propose a different method, based on "inverse" multipole moments, enabling an expansion that converges everywhere. These moments are defined by inverse (i.e., negative) powers of the magnitude of the position vector describing the electron density inside the atom. We illustrate this technique on nitrogen in N(2), oxygen in H(2)O, and oxygen in the phenolic group of the amino acid tyrosine. The proposed method constitutes a considerable advance over the method presented in Part I.     

Transport and Helfand moments in the Lennard-Jones fluid. II. Thermal conductivity

The thermal conductivity is calculated with the Helfand-moment method in the Lennard-Jones fluid near the triple point. The Helfand moment of thermal conductivity is here derived for molecular dynamics with periodic boundary conditions. Thermal conductivity is given by a generalized Einstein relation with this Helfand moment. The authors compute thermal conductivity by this new method and compare it with their own values obtained by the standard Green-Kubo method. The agreement is excellent.     

Calculation of molecular electric polarizabilities and dipole moments. II. The LiH molecule

We use a variation–perturbation method to calculate the electric polarizabilities and the electric dipole moment of the LiH molecule. We obtain 4.455 for the perpendicular polarizability and 4.001 (×10^?24 cm³) for the parallel polarizability. Our result for the electric dipole moment at equilibrium nuclear distance is 5.866, which is in excellent agreement with the experimental value 5.828 debye units.     

Study of correlation holes. II. CI calculations on model polyatomic systems

The shape of correlation holes in many-electron systems is at present scarcely known, even where correlated wave functions are available. We investigate here the kind of electron correlation brought about by configuration interaction (CI ), within a given basis set, in the wavefunction of a polyatomic system. The model ring system H₆ (in two different bonding circumstances) and H₁₄ have been chosen for a detailed study, because of their paradigmatic importance. We set out the equal-spin and different-spin correlation holes as obtained from complete CI calculations in H6 and partial ct in H₁₄, both within a minimal basis set. We basically find the spinless correlation as being short range, while the spin-dependent correlation holes show long-range oscillations of antiferromagnetic character. We also present a natural spin-geminal analysis of the two-body reduced density matrices in these systems; we find a peculiarity possibly related to the long-range correlation discussed above. Finally, we compare the electron correlation as given from our CI wavefunction to other pictures of electron correlation, as obtained essentially from alternant molecular orbital wave functions and from the electron–gas literature.     

Calculation of EPR g tensors for transition-metal complexes based on multiconfigurational perturbation theory (CASPT2).

The computation of the electronic g tensor by two multireference methods is presented and applied to a selection of molecules including CN, BO, AlO, GaO, InO, ZnH, ZnF, O(2), H(2)O(+), O(3) (-), and H(2)CO(+) (group A) as well as TiF(3), CuCl(4) (2-), Cu(NH(3))(4) (2+), and a series of d(1)-MOX(4) (n-) compounds, with M=V, Cr, Mo, Tc, W, Re and X=F, Cl, Br (group B). Two approaches are considered, namely, one in which spin-orbit coupling and the Zeeman effect are included using second-order perturbation theory and another one in which the Zeeman effect is added through first-order degenerate perturbation theory within the ground-state Kramers doublet. The two methods have been implemented into the MOLCAS quantum chemistry software package. The results obtained for the molecules in group A are in good agreement with experiment and with previously reported calculated g values. The results for the molecules in group B vary. While the g values for the d(1) systems are superior to previous theoretical results, those obtained for the d(9) systems are too large compared to the experimental values.     

Ground and lowest-lying electronic states of CoN. A multiconfigurational study

The lowest-lying X1Sigma+, a3Phi, b3II, c5Delta, A1Phi, and B1II electronic states of CoN have been investigated at the ab initio MRCI and MS-CASPT2 levels, with extended atomic basis sets and inclusion of scalar relativistic effects. Among the singlet states, the A1Phi and B1II states have been described for the first time. Potential energy curves, excitation energies, spectroscopic constants, and bonding character for all states are reported. Comparison with other early transition-metal nitrides (ScN, TiN, VN, and CrN), isoelectronic (NiC) and isovalent (RhN and IrN) species has been made, besides analyzing the B1II <=> X1+ electronic transition in terms of Franck-Condon factors, Einstein coefficients, and radiative lifetimes. At both levels of theory, the following energetic order has been obtained: X1Sigma+, a3Phi, b3II, c5Delta, A1Phi, and B1II, with good agreement with experimental results. In contrast, previous DFT and MRCI calculations predicted the ground state to be the 5Delta state.     

Approximate Self-Consistent Molecular Orbital Theory II. CNDO-MO Calculation of Methane Chlorine Derivatives

The CNDO-MO method with s-p separation model modification described in our former work¹⁾ is used here. Methane and it's chlorine derivatives are selected as the model molecules for such calculation. The nuclear coordinates are chosen from microwave spectroscopic data²⁾. Both the self consistent behavior and the invariance of orthogonal transformation²⁾ are quite successfully by preformed through the computation procedure. The ionization potentials predicted by Koopmans' theorem are reasonably good. The charge distribution and dipole moments of each case are calculated, and the results obtained by variation of bond parameter β are compared with the available experimental data satisfactorily.     

Connected moments expansion calculations of the correlation energy in small molecules

The second-order connected moments expansion (CMX(2)) approach to calculation of the correlation energy is tested numerically on several closed-shell di- and tri-atomic molecules. Benchmark computations performed within 6–31G⁷ basis set reveal that CMX(2) usually recovers more than 50% of the MP3 correlation energy and improves the SCF molecular geometries at a cost comparable to the MP3 calculations.     

A note on the convergence of multiconfigurational many-body perturbation theory

The convergence of multiconfigurational many-body perturbation theory (MC MBPT ) is discussed in connection with the intruder state. Its convergence properties are first examined with a fictitious three-level system employing a Hermitian version of MC MBPT , which permits a general model space. It is then applied to the H₂—H₂ and N₂ systems. The results suggest that a more extensive model space is likely to embrace new intruder states and the space extension be executed with due caution.