SCF Wavefunctions Research Articles

Nature of partial sigma bond.

This study investigates the formation of partial sigma (σ) covalent bonds in experimentally synthesizable biradicals formed from hydrogenated and fluorinated C8, C20, and C60 cage structures, by assessing their stability, geometry, and bonding character in singlet and triplet states using restricted B3LYP-D3/6-31+G(d,p) theory, natural bond orbital (NBO) analysis, and complete active space self-consistent field (CASSCF) method. The results show that these partial σCC bonds have Wiberg bond orders of 0.38 to 0.48 and bond lengths ranging from 2.62 Å to 5.93 Å. Cage size influences the characteristics of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), with electrons favoring more antibonding orbitals in smaller cages where electrons reside more on the exterior of the cage and favoring bonding orbitals in larger ones where electrons are more in the interior. Fluorination enhances electron density on bonding orbitals. The analysis further clarified that the differentiation between antibonding and bonding features of HOMOs and LUMOs extends beyond merely electron transfer from s- to p-atomic orbitals, also noting possible interactions of the same symmetry repel. The study also introduces hyperconjugation from α-position CH bonds as a factor in stabilizing partial σ-bond formation. The results also caution against the use of broken symmetry methodology in unrestricted SCF wavefunctions for biradicals, such as those in this study as it may cause large spin contamination and thus errors in the calculated electronic properties results.

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures.

In this work, three versions of self-consistent field/Kohn-Sham density functional theory (SCF/KS-DFT) orbital optimization are described and benchmarked. The methods are a modified version of the geometry version of the direct inversion in the iterative subspace approach (which we call r-GDIIS), the modified restricted step rational function optimization method (RS-RFO), and the novel subspace gradient-enhanced Kriging method combined with restricted variance optimization (S-GEK/RVO). The modifications introduced are aimed at improving the robustness and computational scaling of the procedures. In particular, the subspace approach in S-GEK/RVO allows the application to SCF/KS-DFT optimization of a machine learning technique that has proven to be successful in geometry optimizations. The performance of the three methods is benchmarked for a large number of small- to medium-sized organic molecules, at equilibrium structures and close to a transition state, and a second set of molecules containing closed- and open-shell transition metals. The results indicate the importance of the resetting technique in boosting the performance of the r-GDIIS procedure. Moreover, it is demonstrated that already at the inception of the subspace version of GEK to optimize SCF wave functions, it displays superior and robust convergence properties as compared to those of the standard state-of-the-art SCF/KS-DFT optimization methods.

Synthesis of a Neutral Mononuclear Four-Coordinate Co(II) Complex Having Two Halved Phthalocyanine Ligands That Shows Slow Magnetic Relaxations under Zero Static Magnetic Field.

Syntheses of a novel pseudotetrahedral four-coordinate mononuclear Co(II) complex that has two halved phthalocyanine moieties as the ligands, [Co(half-Pc)2] (1), and its magnetic properties as a single molecule magnet (SMM) are reported. A one pot reaction of phthalonitrile and lithium methoxide followed by the coordination to a Co(II) ion gave 1 as an orange solid in a moderate yield. X-ray crystallography on 1 reveals tetragonally distorted coordination geometry around the Co(II) ion. The M- HT-1 plots suggest that 1 has large axial magnetic anisotropy. The ac magnetic susceptibility data of the magnetically diluted 1 (dil.1) clearly show that the complex acts as an SMM even in the absence of the external static magnetic field ( Hdc). The influence of intermolecular and intramolecular interactions for the magnetic relaxation behaviors has been discussed by comparison of the magnetic data of 1 and dil.1. The Orbach process is suggested as the predominant mechanism of magnetic relaxations in the high-temperature range, and the Arrhenius plots provide the effective relaxation energy barrier and pre-exponential factor of Ueff = 54.0 cm-1 and τ0 = 3.17 × 10-10 s, respectively. The direct estimation of the axial anisotropic parameter of 1 was successfully performed by high-field, multifrequency ESR measurements up to 55 T and 2.5 THz. The evaluated axial zero-field splitting (ZFS) energy of 57.0 cm-1 is comparable to the Ueff energy, confirming that the magnetic relaxations are initiated by the thermal excitation from the ground | M S⟩ = |±3/2⟩ states to the |±1/2⟩ states in the high-temperature range. The results of the ab initio calculations based on the CAS(7,5) SCF wave functions indicate that the ground states of 1 consist mainly of | M S⟩ = |±3/2⟩ states, while the first excited states are the mixture of | M S⟩ = |+1/2⟩ and |-1/2⟩.

Diagonalization of large matrices: a new parallel algorithm.

On the basis of a dressed matrices formalism, a new algorithm has been devised for obtaining the lowest eigenvalue and the corresponding eigenvector of large real symmetric matrices. Given an N × N matrix, the proposed algorithm consists in the diagonalization of (N - 1)2 × 2 dressed matrices. Both sequential and parallel versions of the proposed algorithm have been implemented. Tests have been performed on a Hilbert matrix, and the results show that this algorithm is up 340 times faster than the corresponding LAPACK routine for N = 10(4) and about 10% faster than the Davidson method. The parallel MPI version has been tested using up to 512 nodes. The speed-up for a N = 10(6) matrix is fairly lineal until 64 cores. The time necessary to obtain the lowest eigenvalue and eigenvector is nearly 5.5 min with 512 cores. For an N = 10(7) matrix, the speed-up is nearly linear to 256 cores and the calculation time is 5.2 h with 512 nodes. Finally, in order to test the new algorithm on MRCI matrices, we have calculated the ground state and the π → π* excited state of the butadiene molecule, starting from both SCF and CASSCF wave functions. In all the cases considered, correlation energies and wave functions are the same as obtained with the Davidson algorithm.

Particle correlation from uncorrelated non Born–Oppenheimer SCF wavefunctions

We analyse a nonadiabatic self-consistent field method by means of an exactly-solvable model. The method is based on nuclear and electronic orbitals that are functions of the cartesian coordinates in the laboratory-fixed frame. The kinetic energy of the center of mass is subtracted from the molecular Hamiltonian operator in the variational process. The results for the simple model are remarkably accurate and show that the integration over the redundant cartesian coordinates leads to couplings among the internal ones.

Natural hybrid orbitals: Ab initio SCF and CI results for CO and NiCO

The natural hybrid orbital (NHO) procedure of Foster and Weinhold is generalized to treat ab initio SCF or CI wavefunctions in minimal or extended basis sets. The first applications of the ab initio NHO analysis to a series of wavefunctions for carbon monoxide and the NiCO complex are presented. Numerical and graphical comparisons of NHOs for these systems exhibit the effects of basis-set augmentation and electron correlation on the details of the natural “Lewis diagrams”. Hybrid p-character and bond polarization are found to be persistent features of the NHO description, well represented even at the minimal basis level. Extension of the basis set allows the natural lone pairs to delocalize somewhat, while the principal effect of electron correlation is to shift occupancy somewhat into the π*CO orbitals. The effect of coordination of CO to a Ni atom, as conventional chemical intuition would suggest, is to polarize the carbon lone pair more toward the metal atom and the πCO bond more toward the oxygen.

Partial photoionization cross sections and radiative recombination rate coefficients for Li-like ions. II

A nonhydrogenic single-electron-transition model with Dirac-Slater SCF wavefunctions and all necessary multipoles has been used to obtain partial photoionization cross sections for C3+, O5+, Al10+, Fe23+, and Mo39+ for principal quantum number n = 10 and all l, hv ⪖ 200 keV, supplementing results reported elsewhere for n = 2, 3, 4, and 6. The partial cross sections for the isoelectronic sequence are represented approximately by a simple analytical form: ln[(Z — snl)2 σnl (hv)] = Σai(nl)xi. (Z is the nuclear charge, x = ln [hv/(Z — 2)2].) n-3 scaling is used to obtain partial cross sections for other values of n (6 < n < 10, 10 < n < 100). Radiative recombination rate coefficients (summed over l and n < 100) have been calculated from the partial photoionization cross sections for kT = 0.01, 0.03, 0.1, 0.3, 1.0, 3.0, and 10.0 keV. The results have application to ionization balance calculations for the solar corona and for Tokamaks.

All-electron calculations of open-shell polyatomic molecules I. SCF wave function in gaussians for methyl and vinyl radicals

An all-electron MO calculation in Gaussian functions is presented for the methyl radical and its ions and the vinyl radical. Roothaan's open-shell technique, using two effective Hamiltonians, is applied for solving the LCAO-SCF equations.

Comparison for pyrrole and pyrazole of orbital energies and population analyses from ab-initio SCF, CNDO/2, INDO, extended hückel, and ARCANA calculations

The results of our recent ab-initio SCF calculations on pyrrole and pyrazole using large Gaussian basis sets are compared to those using less rigorous methods: CNDO/2, INDO, PCILO extended Huckel, and ARCANA (a type of iterative extended Huckel calculation). The ab-initio orbital energies are higher in energy than all those resulting from less rigorous methods. For the two highest occupied orbitals, both of π type, (pyrrole— 1a2 and 2b1; pyrazole—3a″ and 2a″) there was excellent agreement between the measured photoelectron spectroscopic ionization potentials and the Koopman's theorem values from the ab-initio results. Thus the orbital energies calculated by the less rigorous methods all lie too low in energy. The CNDO/2 and INDO orbital energies also span too large a width for the valence band compared to the ab-initio results. The gross atomic populations from the CNDO/2, INDO and PCILO methods show discrepancies from the ab-initio results for both the heteroatoms and the hydrogens. Total overlap populations calculated from the ab-initio SCF wave functions show large negative overlap populations between nonbonded ring atoms. Using the off-diagonal density matrix elements from CNDO/2 and INDO wave functions as if they were true off-diagonal elements from non-ZDO calculations, scaling them (shown previously to lead to reasonable values for TOPS between bonded atoms) led to TOPS between nonbonded ring atoms that were essentially zero. Wiberg bond indices, by definition only capable of giving positive numbers, also cannot reproduce these negative overlap populations. The extended Huckel and ARCANA methods, which are non-ZDO methods, both gave negative tops between nonbonded ring atoms, although not as large as those which resulted from ab-initio calculations.

The accuracy of molecular bond lengths computed by multireference electronic structure methods

We compare experimental R e values with computed R e values for 20 molecules using three multireference electronic structure methods, MCSCF, MR-SDCI, and MR-AQCC. Three correlation-consistent orbital basis sets are used, along with complete basis set extrapolations, for all of the molecules. These data complement those computed previously with single-reference methods. Several trends are observed. The SCF R e values tend to be shorter than the experimental values, and the MCSCF values tend to be longer than the experimental values. We attribute these trends to the ionic contamination of the SCF wave function and to the corresponding systematic distortion of the potential energy curve. For the individual bonds, the MR-SDCI R e values tend to be shorter than the MR-AQCC values, which in turn tend to be shorter than the MCSCF values. Compared to the previous single-reference results, the MCSCF values are roughly comparable to the MP4 and CCSD methods, which are more accurate than might be expected due to the fact that these MCSCF wave functions include no extra-valence electron correlation effects. This suggests that static valence correlation effects, such as near-degeneracies and the ability to dissociate correctly to neutral fragments, play an important role in determining the shape of the potential energy surface, even near equilibrium structures. The MR-SDCI and MR-AQCC methods predict R e values with an accuracy comparable to, or better than, the best single-reference methods (MP4, CCSD, and CCSD(T)), despite the fact that triple and higher excitations into the extra-valence orbital space are included in the single-reference methods but are absent in the multireference wave functions. The computed R e values using the multireference methods tend to be smooth and monotonic with basis set improvement. The molecular structures are optimized using analytic energy gradients, and the timings for these calculations show the practical advantage of using variational wave functions for which the Hellmann–Feynman theorem can be exploited.

Photoactivated excited states of DNA repair photolyase: Dynamical and semiempircal identification

AbstractDNA damage caused by UV light radiation is often naturally repaired in a process initiated by excited state electron transfer from the photoactivated photolyase enzyme to the DNA cyclobutane pyrimidine dimer lesion. The active cofactor in the excited state electron transfer in the photolyase is the two‐electron fully reduced form of the flavin adenine dinucleotide (FADH−). To calculate electron tunneling matrix element and model the DNA binding with photolyase, the LUMO of the FADH− calculated using extended Huckel method was previously chosen from the SCF wavefunctions. Recently, the DNA–photolyase complex was crystallized in its bound form, in good agreement with our previous model in even minute details at the active site. Here we carry out molecular dynamics simulation of the entire complex using the new experimental structure of Anacystis nidulans and identify the low‐lying photoactivated states of the enzyme for the dynamical confirmations. Our results from ZINDO/S CIS calculations are compared with experimental UV spectra, and their implications for excited state electron transfer and energy transfer are discussed. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

MNDO parameterized hybrid SLG/SCF method as used for molecular modeling of Zn(II) complexes

AbstractThe McWeeny's group functions technique is a natural way to introduce local description into quantum chemistry. It can also serve as a basis for constructing numerically effective computational schemes with almost linear scaling of computational costs with the size of a system. In this study, we apply it to the coordination compounds of Zn(II)‐containing ligands with nitrogen and oxygen donor atoms. In these compounds, the electron group corresponding to the metal vacant 4s‐ and 4p‐atomic orbitals (AOs) of the Zn2+ ion and its closest coordination sphere formed by the lone pairs (LP) located on the donor atoms naturally separates. This group, designated metal and lone pairs (MLP), is described by the SCF wave function within the hybrid scheme of strictly local geminals/self‐consistent field (SLG/SCF). The SLC/SCF scheme is based on the group function approach combining different descriptions for different electron groups: two‐electron two‐center bonds are described by geminals (SLG groups), while all the remaining electron groups are described by Slater determinants in the one‐electron (SCF) approximation (SCF groups). The original MNDO Hamiltonian parameterization for the Zn atom is adjusted for correct description of geometry of the complexes. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

FRODO: a MuPAD program to calculate matrix elements between contracted wavefunctions

A symbolic program performing the Formal Reduction of Density Operators (FRODO) has been developed in the MuPAD computer algebra system with the purpose of evaluating the matrix elements of the electronic Hamiltonian between internally contracted functions in a complete active space (CAS) scheme. The program is illustrated making use of two meaningful examples. Program summary Title of program:FRODO Catalogue identifier:ADVY Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVY Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer:Any computer on which the MuPAD computer algebra system can be installed Operating systems under which the program has been tested:Linux Programming language used:MuPAD vs. 2.5.3 for Linux No. of lines in distributed program, including test data, etc.:3939 No. of bytes in distributed program, including test data, etc.:19 661 Distribution format:tar.gz Nature of physical problem: In order to improve on the CAS–SCF wavefunction one can resort to multireference perturbation theory or configuration interaction based on internally contracted functions (ICF) which are obtained by application of the excitation operators to the reference CAS–SCF wavefunction. The formulation of such matrix elements is quite cumbersome and a computer algebra system like MuPAD appears ideally suited to perform such a task. Method of solution: The method adopted consists in successively eliminating all occurrences of inactive orbital indices (core and virtual) from the products of excitation operators which appear in the definition of the ICF's and in the electronic Hamiltonian expressed in the second quantization formalism. Restrictions due to the complexity of the problem: The program is limited to no more than doubly excited ICF's.

Intramolecular Charge-Transfer State Formation of 4-(N,N-Dimethylamino)benzonitrile in Acetonitrile Solution: RISM-SCF Study

Intramolecular charge-transfer (ICT) state formation of 4-(N,N-dimethylamino)benzonitrile in acetonitrile solution is studied by the reference interaction site model self-consistent field (RISM-SCF) method. Geometry optimizations are performed for each electronic state in solution with the complete-active-space SCF wave functions. Dynamic electron correlation effects are taken into account by using the multiconfigurational quasidegenerate perturbation theory. Two-dimensional free energy surfaces are constructed as the function of the twisting and wagging angles of the dimethylamino group for the ground and locally excited (LE) states. The calculated absorption and fluorescence energies are in good agreement with experiments. The validity of the twisted ICT (TICT) model is confirmed in explaining the dual fluorescence, and the possibility of the planar ICT model is ruled out. To examine the mechanism of the TICT state formation, a "crossing" seam between the LE and charge-transfer (CT) state surfaces is determined. The inversion of two electronic states occurs at a relatively small twisting angle. The effect of solvent reorganization is also examined. It is concluded that the intramolecular twisting coordinate is more important than the solvent fluctuation for the TICT state formation, because the energy difference between the two states is minimally dependent on the solvent configuration.

Ab initio study of the torsional potential for 9-phenylanthracene in the ground and excited states

Torsional potentials of 9-phenylanthracene both in the ground and excited states were determined by using ab initio molecular orbital calculations. Molecular structure in the ground state was optimized at the restricted Hartree–Fock level under the C 2 v symmetry. Then, the torsional potentials between the anthracene ring and the phenyl group in the S 0 and S 1 states were calculated by means of multi-reference perturbation theory based on the complete active space (CAS) SCF wave function. The present findings were consistent with the jet-laser experimental results by Barbara et al.

The equilibrium geometry of the SC3H radical: an ab initio study

The SC3H radical is known by experiment to have a linear equilibrium structure, but even rather high-level ab initio computations give a bent equilibrium geometry. A theoretical study of the SCCCH radical has been carried out in order to analyse the influence of several factors in the computed equilibrium structure. Quadratic configuration interaction QCISD(T) and restricted coupled cluster RCCSD(T) computations have been performed in combination with large basis sets. Spin-orbit effects have been taken into account through the Breit-Pauli Hamiltonian using multi-configuration SCF and configuration interaction wavefunctions. Our final results indicate that the equilibrium structure must be linear, in agreement with the experimental studies [McCarthy, M. C., Vrtilek, J. M., Gottlieb, C. A., Wang, W., and Thaddeus, P., 1994, Astrophys. J., 431, L127; Hirahara, Y., Ohshima, Y, and Endo, Y, 1994, J. chem. Phys., 101, 7342]. Both spin-orbit and electron correlation effects appear to be of comparable importance, but an adequate computation of the correlation energy has been much more difficult and has ultimately required basis set extrapolations.

Valence orbital electron momentum distributions for dimethylsulfide: comparison of EMS measurements with near Hartree–Fock limit and density functional theory calculations

The binding energy spectra and orbital electron momentum density distributions of the complete valence shell of (CH 3) 2S have been measured by electron momentum spectroscopy at a total energy of 1200 eV+binding energy. Binding energies for the three inner valence (6a 1, 3b 2 and 5a 1) orbitals which have not been well characterized by photoelectron spectroscopy have been assigned in the present work. The extensive structure observed in the high energy region from 30 to 55 eV is attributed to satellite peaks from the inner valence orbitals. Measured electron momentum profiles for each of the valence orbitals are compared with calculations using the target Hartree–Fock approximation and SCF wavefunctions with a range of basis sets up to the large, saturated and diffuse aug-cc-pV5Z basis set. The observed momentum profiles are also compared with DFT momentum profiles calculated using the target Kohn–Sham approximation with the B3LYP and B3PW91 gradient corrected functionals. Individual experimental and calculated momentum profiles are presented for the three outermost orbitals (3b 1, 8a 1 and 5b 2) while the summed experimental data and calculations are presented for the four closely-spaced 1a 2, 4b 2, 7a 1 and 2b 1 higher binding energy orbitals in the outer valence region. Experimental and theoretical momentum profiles for the three inner valence orbitals are also presented. In general, both the Hartree–Fock and DFT calculations with high-level basis sets give good descriptions of the experimental electron momentum profiles.

Perturbative corrections to the equation-of-motion spin–flip self-consistent field model: Application to bond-breaking and equilibrium properties of diradicals

We present perturbative corrections to a recently introduced spin–flip self-consistent field (SF-SCF) wave function. The spin–flip model describes both closed and open shell singlet states within a single reference formalism as spin–flipping, e.g., α→β, excitations from a triplet (Ms=1) reference state for which both dynamical and nondynamical correlation effects are much smaller than for the corresponding singlet state. The simplest spin–flip model employs a SCF wave function for the reference state, and the resulting equations for target states are therefore identical to configuration interaction singles (in spin–orbital form). While being a qualitatively correct zero-order wave function, SF-SCF should be augmented by dynamical correlation corrections to achieve a quantitative accuracy. The results demonstrate that the second-order approximation to the more theoretically complete spin–flip coupled-cluster model (truncated at double substitutions) represents a systematic improvement over the SF-SCF model.

Parity-violating energy of d-glyceraldehyde

Parity-violating interaction energy ( E pv) of d-glyceraldehyde was calculated by using the spin–orbit coupling SCF wavefunction and the 5s2p basis set. The E pv value was negative for most of the low-energy conformations of d-glyceraldehyde, suggesting that d-glyceraldehyde is more stable than l-glyceraldehyde due to the parity-violating weak neutral current interaction.

Parity-violating energy for the chirality-producing step in Strecker synthesis of l-alanine

The potential energy curve for the reaction of the ethaniminium ion (CH3CHNH2+) and the cyanide anion (CN−) to give 2-amino-propanenitrile (APN) in aqueous solution which is the chirality-producing step of Strecker synthesis of l-alanine was obtained by ab initio GB 6-31G∗∗ calculation including the solvent effect. The transition state was located at 2.13Å of the Cα–C(N) distance. The barrier height for this reaction was 16.6kcal/mol and the reaction is expected to occur easily in aqueous solution. The parity-violating interaction energy (Epv) was calculated by using the spin–orbit-coupling SCF wavefunction and the [5s2p1d/3s1p] basis set. The Epv value of the association state of the two ions is zero, while the reaction product l-APN has the positive value of +0.17×10−20hartree. Epv was positive for all reaction stages including the transition state, suggesting that the formation of l-APN is not more favorable than d-APN in the Strecker synthesis of alanine due to the parity-violating weak neutral current interaction.