SCF Wavefunctions Research Articles

Theoretical Study of Oxocyclohexadienylidene Isomers: Electronic Structures and Molecular Properties

The molecular properties and electronic structures for three isomers of oxocyclohexadienylidene were investigated using multiconfiguration SCF (MCSCF) wave functions. The ground electronic states of the ortho and para isomers are the open shell triplet, whereas the meta isomer has a singlet ground state with significant open shell character. The structural features of the ground states of all three isomers are close to the quinoid type structure. Several molecular properties such as the electron spin density, electron affinity (EA), acidity and bond dissociation energy for the three isomers and/or their corresponding radicals are also considered and are compared with experimental values. In particular, the MCSCF(8,8)/6-31+G* electron spin densities for both ortho and para isomers are very close to the experimental values of the phenoxyl radical.

Ground and excited states of the Ne +3 molecule

Quantum-chemical ab initio calculations were performed for the electronic ground state and several low-lying excited states of the Ne 3 + molecular ion. Large parts of the potential energy surfaces, including the global minimum of the ground state, were treated by means of multi-reference many-body perturbation theory, starting from the SCF wave function of neutral Ne 3. For the inductive local minima of the ground state at C ∞v and C 2v geometries, the multi-configuration coupled electron-pair approach was used, together with an extended basis set. In agreement with the best previous calculations, we obtain a symmetric linear (D ∞h) equilibrium geometry for the Ne 3 + ground state, with a bond distance of 3.55 a.u. and a binding energy of 0.10 eV relative to Ne 2 + and Ne. In addition to this global minimum, two local minima exist, which correspond to a Ne 2 + ion in its electronic ground state ( R e=3.27 a .u.) binding a Ne atom by inductive forces. Both these minima are very shallow (0.07 and 0.03 eV for the C ∞v and C 2v structures). Potential energy surfaces for several low-lying excited states of Ne 3 + were calculated as well and their properties, e.g. adiabatic and vertical excitation energies, local minima, and dissociation channels, are discussed.

Ab initio determination of a rather accurate force constant for a given wave function

In this research, an attempt has been made to modify present methods of force constant calculation to have a rather simple and accurate procedure in order to check the accuracy of a given ab initio wave function. After a brief survey of literature, it is found that at neighborhood of equilibrium the bottom of potential surface, which is potential curve in two-dimensional space, is not exactly quadratic, in spite of its appearance, which looks like parabola. Nth degree polynomial must be fitted to different points of potential curve, which are obtained by an ab initio total energy calculation. The obtained polynomial is the best potential for a given ab initio wave function, and can predict a rather accurate force constant and bond length belonging to the corresponding wave function. It is also found that a particular n-degree polynomial cannot be generalized and used for any molecule. Additionally, in order to reduce the percentage of error in evaluation of force constant, it has been demonstrated that the selection of basis set is important. The force constant for diatomic molecules such as H2, LiH and BH obtained by FSGO wave functions are 6.189mdyne/Å (7.22%), 1.063mdyne/Å (3.61%) and 3.189mdyne/Å (4.77%), respectively. While the corresponding values calculated by using total energies obtained by SCF wave function for basis set RHF/6-311G∗∗ are 6.283mdyne/Å (8.71%), 1.061mdyne/Å (3.04%) and 3.359mdyne/Å (10.35%), respectively. These values are also compared with those of gaussian 98 program (Pople's package), which are 12.55mdyne/Å (117.13%), 1.361mdyne/Å (32.70%) and 3.971mdyne/Å (30.45%), respectively. The method is used for determination of krr and kθθ of H2O, when the FSGO method is used: they are 7.98mdyne/Å (−5.56%) and 1.30mdyne/Å (70.13%), respectively, and when gaussian 98 package is used: they are 9.76mdyne/Å (15.52%) and 2.79mdyne/Å (267.0%), respectively. Our method is also compared with the force method (Pulay). It is demonstrated that the proposed method gives less error for non-exact wave functions than those of force method. Then it can be applied for both exact and non-exact wave functions.

Critical assessment of the hybrid QM/MM-pol-vib approach: Small water clusters using polarizable flexible water potentials

We report a systematic study of the structure of small water clusters, up to pentamers, using a hybrid quantum-mechanics/molecular-mechanics approach with polarizable flexible water-interaction potentials in conjunction with HF SCF wave functions. The model is denoted QM/MM-pol-vib. For each optimized QM cluster, we replaced QM water molecules one at a time with MM-pol-vib water molecules and reoptimized the cluster structure. We found that the hybrid structures and energies reproduce well their full QM counterparts. This finding indicates that the first hydration shell of solvation obtained with such a model is described at a semiquantitative level of accuracy. The model should prove useful in modeling aqueous reactions. We outline the efficient computational strategy adopted for coupling the polarizable response of the solvent with the solute wave function calculation. Energy gradients for the solute and the solvent molecules are also efficiently calculated. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 199–210, 2000

Theoretical studies on the nonlinear optical properties of zwitterionic organic molecules: effect of π–σ–π through-bond coupling on the first hyperpolarizability

First hyperpolarizabilities ( β) have been calculated by time-dependent Hartree–Fock (TDHF) formalism using the ab initio SCF wavefunctions for some zwitterionic organic molecules containing a π-electron donor and π-electron acceptor separated by saturated C–C σ-bonds (saturated bridges). The geometries of the molecules have been optimized using HF/6-31G basis sets. Charge transfer is observed even when the donor and acceptor are separated by more than one σ-bond, giving rise to a large first hyperpolarizability. This study suggests that these bridges may have potential applications in the development of nonlinear optical materials.

Three Lowest-Lying Electronic States of NH2

The three lowest-lying electronic states, X̃ 2B1, à 2A1, and B̃ 2B2, as well as the lowest linear 2Π stationary point of NH2 have been investigated systematically using ab initio electronic structure theory. The SCF, CASSCF, CISD, CASSCF-SOCI, CCSD, and CCSD(T) levels of theory have been employed to determine total energies, equilibrium structures, and physical properties including dipole moments, harmonic vibrational frequencies, and infrared intensities of NH2. According to the instability analysis of the reference SCF wave functions, physical properties of the three lowest-lying equilibrium states of NH2 may be obtained correctly in the variational sense with all wave functions employed in this study. The lowest linear stationary point (2Π) possesses two distinct imaginary vibrational frequencies along the bending coordinate, indicating a strong Renner−Teller interaction. The predicted geometries and physical properties of the two lowest states of NH2 are in good agreement with available experimental results. At the CCSD(T) level of theory with the largest basis set, the triple-ζ (TZ) plus triple polarization with two sets of higher angular momentum and two sets of diffuse functions [TZ3P(2f,2d)+2diff], the à 2A1 state of NH2, with a large bond angle of 144.9°, is predicted to lie 32.1 kcal/mol (1.39 eV, 11 200 cm-1) above the ground state. This is in excellent agreement with the experimental T0 value of 31.80 kcal/mol (1.379 eV, 11 122.6 cm-1). The second excited state (B̃ 2B2) possesses an acute bond angle of 49.3° and is determined to lie 100.1 kcal/mol (4.34 eV, 35 000 cm-1) above the ground state. The classical (and effective) barriers to linearity for the X̃ 2B1 and à 2A1 states were predicted to be 11 870 (12 310) cm-1 and 720 (790) cm-1, which are again in good accord with the experimentally estimated values of 12 024 cm-1 (X̃ 2B1) and 730 cm-1 (à 2A1).

Adiabatic correction to the energy of molecular systems: the CPHF equivalent of the Born–Handy formula

The Born–Handy formula, recently shown by Kutzelnigg to be a rigorous expression for the calculation of the adiabatic correction, has been, on the level of a ground state SCF wavefunction, reformulated and linked to the coefficients of the standard coupled perturbed Hartree–Fock (CPHF) method. The contribution of the electron correlation via second-order perturbation theory is also presented. The solution of the corresponding secular equation of the nuclear motion enables the calculation of the adiabatic correction over the particular normal modes. The method offers the possibility of extending high-precision calculations of the adiabatic correction to more complex systems. Test calculations have been performed for H 2, HD and D 2 and the results are in satisfactory agreement with the exact figures.

Covalent bond orders and atomic valences from correlated wavefunctions

A comparison is made between two alternative definitions for covalent bond orders: one derived from the exchange part of the two-particle density matrix and the other expressed as the correlation of fluctuations (covariance) of the number of electrons between the atomic centers. Although these definitions lead to identical formulae for mono-determinantal SCF wavefunctions, they predict different bond orders for correlated wavefunctions. It is shown that, in this case, the fluctuation-based definition leads to slightly lower values of the bond order than does the exchange-based definition, provided one uses an appropriate space-partitioning technique like that of Bader's topological theory of atoms in a molecule; however, use of Mulliken partitioning in this context leads to unphysical behaviour. The example of H 2 is discussed in detail.

Continuous symmetry measures for electronic wavefunctions

A continuous symmetry measure (CSM) which gives the magnitude of the deviation of an electronic wavefunction from a given symmetry element S is derived from the quantum mechanical expectation value of a symmetry operator Ŝ. The functional is normalized in the interval [0,100], i.e. CSM ( S ̂ )=0 means that Ŝ commutes with the Hamiltonian. Intermediate values indicate the percentage deviation of the wavefunction from the corresponding symmetry. First applications of the method using ab initio Hartree–Fock SCF, density functional and semi-empirical AM1 wavefunctions are presented to quantify the chirality (degree of deviation from improper rotational symmetry) of organic molecules.

Halogen Nuclear Quadrupole Coupling Constants: Comparison of ab initio Calculations which include Correlation, with Experiment

Abstract Ab initio determination of the electric field gradient (EFG) tensors at halogen and other centres ena-bled determination of the nuclear quadrupole coupling constants (NQCC) for a diverse set of axially symmetric (C3v , C∞v, D∞h and other symmetries) inorganic and organic molecules, where the heavy ele-ments are Cl, Br, and I with C, Si, Ge, and Sn hydrides. The latter elements are in an approximately tetrahedral environment. The study presents results at a standardised level of calculation, triple-zeta in the valence space (TZV) plus polarisation functions (TZVP) for the equilibrium geometry stage; all-electron MP2 correlation is included in all these studies. f-Orbital exponents were optimised for both Br and I centres in the methanes; the atomic populations of the f-orbital components are very small for the Br-and I-atoms, confirming their role as polarisation functions rather than having any bonding character. The EFG are determined at equilibrium with the TZVP basis set, except Sn and I centres where the basis set is TZV + MP2. For the bromo and iodo compounds, especially the latter, it is essential to allow for core polarisation, by decontraction of the p,d-functions. This is conveniently done by initial optimization of the structure with a partly contracted basis, followed by reestablishment of the equilibrium structure with the decontracted basis. A close correlation of the observed (microwave spectral) data with the calculations was observed, using the 'best' values for the atomic quadrupole moments for Cl, Br, and I; thus there seems no need to postulate that the value of QBr for 79Br and 81Br are in error. The SCF and MP2 wave-functions were converted into localised molecular orbitals by the Boys Method. This allowed a study of the differing s/p/d-hybridisation ratios, and the centroid positions, to be compared with the quadrupole coupling constants. The charge distributions for the atoms were converted into local bond dipoles, which in turn are correlated with the electronegativity differences of the bonded atoms.

Imaging of the outer valence orbitals of CO by electron momentum spectroscopy — Comparison with high level MRSD-CI and DFT calculations

A newly constructed energy dispersive multichannel electron momentum spectrometer has been used to image the electron density of the outer valence orbitals of CO with high precision. Binding energy spectra are obtained at a coincidence energy resolution of 1.2 eV fwhm. The measured electron density profiles in momentum space for the outer valence orbitals of CO are compared with cross sections calculated using SCF wavefunctions with basis sets of varying complexity up to near-Hartree-Fock limit in quality. The effects of correlation and electronic relaxation on the calculated momentum profiles are investigated using large MRSD-CI calculations of the full ion-neutral overlap distributions, as well as large basis set DFT calculations with local and non-local (gradient corrected) functionals.

Stationary Points on the Ground-State Potential Energy Surface of Dimethyldiazene. Isomerization and Decomposition in Competition

The singlet ground-state potential energy surface as related to the thermal unimolecular mechanisms of dimethyldiazene was investigated, in order to obtain activation energies for trans−cis isomerization, as well as for the isomerization leading to 1,1-dimethyldiazene and for the simple C−N bond cleavage in the formation of CH3N2• and CH3• radicals. We used approximate density functional theory (DFT) with B3LYP potential to locate minimum energies and transition-state structures, as well as to determine harmonic vibrational frequencies and resulting zero-point vibrational energies. To obtain more reliable results, some structures were reoptimized by the multiconfiguration SCF wave function. The energetics were determined using quadratic configuration interaction singles and doubles (QCISD), perturbation theory with UHF and CAS reference wave functions (MP2-MP4 and CASPT2), and the configuration interaction wave function, which includes single and double excitations from the selected set of reference configurations constructed with the CASSCF molecular orbitals (MR-CISD). In contrast to previous theoretical studies, our results show that the trans−cis isomerization of 1,2-dimethyldiazene, which proceeds by rotation around the NN bond, or semilinearization, requires an activation energy near to that of its decomposition. It was also confirmed that isomerization to 1,1-dimethyldiazene is less favored than the cis−trans isomerization. The following barrier heights have been estimated: 229 kJ/mol for decomposition, 207 kJ/mol for isomerization by rotation, 227 kJ/mol for isomerization by semilinearization, and 424 kJ/mol for rearrangement to 1,1-dimethyldiazene. Calculation of RRKM rate coefficients showed that in the temperature range from 450 to 600 K the trans−cis isomerization and a direct decomposition proceed in competition. However the more stable trans-1,2-dimethyldiazene preferentially decomposes directly, as a consequence of the fast reverse cis−trans isomerization rate. At the temperatures above 600 K a direct decomposition increasingly predominates over isomerization.

Theoretical and (e,2e) Experimental Investigation into the Complete Valence Electronic Structure of [1.1.1]Propellane

An electronic structural study of the complete valence shell of [1.1.1]propellane is reported. Binding energy spectra were measured in the energy regime of 3.5−46.5 eV over a range of different target electron momenta, so that momentum distributions (MDs) could be determined for each ion state. Each experimental electron momentum distribution is compared with those calculated in the plane wave impulse approximation using both a triple-ζ plus polarization level SCF wave function and a further 13 basis sets as calculated using density functional theory. A critical comparison between the experimental and theoretical momentum distributions allows us to determine the optimum wave function for [1.1.1]propellane from the basis sets we studied. In general, the level of agreement between the experimental and theoretical MDs for this optimum wave function for all of the respective valence orbitals is fair. The determination of this wave function then allows us to derive the chemically interesting molecular properties of [1.1.1]propellane. A summary of these results and a comparison of them with those of other workers are presented with the level of agreement typically being good. In particular, we note that we confirm the existence of the C1−C3 bridging bond with a bond order of 0.70.

Modern valence-bond description of the electronic structure of benzocyclobutadiene

The ground state of benzocyclobutadiene, a bicyclic molecule with 8π electrons containing a benzene and a cyclobutadiene ring, is studied by means of modern valence bond (VB) theory in its spin-coupled (SC) form and the complete-active-space self-consistent field (CAS SCF) approach. The CAS SCF wave function is used to optimize the geometry, and SC theory—to obtain a well-correlated and easy to visualize and understand model of the active space hosting the π electrons. It is shown that the π system of the ground state of benzocyclobutadiene can be described with sufficient accuracy as a combination of the π systems of a distorted benzene ring and an isolated double bond. Each of the eight SC orbitals is found to be well-localized about one carbon atom only, with small distortions toward its nearest neighbors. The analysis of the optimal active-space spin-coupling pattern within the SC wave function for benzocyclobutadiene shows unambiguously that this molecule inherits neither the aromatic nor the antiaromatic character of its cyclic components, and it is most appropriate to regard it as nonaromatic. © 1996 John Wiley & Sons, Inc.

MCSCF calculation of the frequency-dependent hyperpolarizability of the lithium atom

mThe second electric dipole hyperpolarizability of the lithium atom is calculated using a series of multiconfiguration SCF wave functions with an increasing number of active space orbitals. In agreement with other recent calculations, we find a very large correlation correction to the hyperpolarizability. We analyze the frequency dependence of the dc Kerr hyperpolarizabily y K( w) = y( - w; w, 0,O) and observe very significant dispersion effects. 0 1996 John Wiley & Sons, Inc.

Modification of the Roothaan equations to exclude BSSE from molecular interaction calculations

The Roothaan equations have been modified to compute molecular interactions between weakly bonded systems at the SCF level of theory without the basis set superposition error (BSSE). The increase in complication with respect to the usual SCF algorithm is negligible. Calculation of the SCF energy on large systems, such as nucleic acid pairs, does not pose any computational problem. At the same time, it is shown that a modest change in basis-set quality from 3-21G to 6-31G changes the binding energy by about 50% when computed according to standard SCF “supermolecule” techniques, while remaining practically constant when computed without introducing BSSE. Bader analysis shows that the amount of charge transferred between the interacting units is of the same order of magnitude when performed on standard SCF wave functions and those computed using the new method. The large difference between the corresponding computed energies is thus ascribed to the BSSE. © 1996 John Wiley & Sons, Inc.

Effect of optimised hybridization displacement charge on the description of molecular electrostatic potentials of some substituted acetaldehydes

Molecular electrostatic potential (MEP) maps of acetaldehyde, fluoroacetaldehyde, trifluoroacetaldehyde, hydroxyacetaldehyde and aminoacetaldehyde were studied usingab initio SCF wavefunctions with 6–31G** basis set as well as a recently developed and optimised new method in which a combination of Lowdin and hybridization displacement charges (HDC) at the MNDO level is used. An important point of this method is the distribution of electronic charges continuously and spherically in three dimensions, which helps reproduce most of the important features of the correspondingab initio MEP maps that cannot be achieved using point charges. Electrophilic reactivity of the molecules has been discussed using the MEP results.

Vibration-rotation levels of water beyond the Born-Oppenheimer approximation

The value of the adiabatic correction to the Born-Oppenheimer electronic energy is calculated as a function of geometry for water using SCF wavefunctions. A mass-dependent adiabatic function is combined with high-accuracy ab initio electronic structure calculations due to Partridge and Schwenke. Vibrational band origins for H 2O, D 2O, T 2O, HDO, HTO and DTO are analysed. Unlike previous calculations on the H 3 + system, it is suggested that non-adiabatic effects are more important than adiabatic surface and effective masses of the heavy particles intermediate between the nuclear and atomic masses is found to significantly improve predictions of rotational term values. The adiabatic correction is found to be of particular importance for rotational levels with high K a.

Orthogonal effective atomic orbitais in the topological theory of atoms

A simple formalism has been developed permitting us to extract, from the molecular wave functions, the effective orthogonal atomic orbitais characterizing the actual state of the atom in the molecule within the framework of Bader's topological theory of atoms. This may give important conceptual connections between the SCF wave functions obtained in the large-scale ab initio calculations, or even at the Hartree–Fock limit, and the traditional atomic orbital picture. The method is based on some partial orthogonality properties of the non-orthogonal localized molecular orbitais constructed by requiring a maximal weight in the given atomic domain, or in another selected molecular fragment. (The use of such localized orbitais may also be of independent interest.) Key words: effective atomic orbitais, atomic orbitais from molecular wave functions, non-orthogonal localized orbitais, topological theory of atoms, Bader's theory of atoms in molecules.

Pair populations and effective valencies from ab initio SCF and spin-coupled wave functions

Pair populations and effective valencies from ab initio SCF and spin-coupled wave functions