Unrestricted Hartree-Fock Orbitals Research Articles

Ab initio spectroscopy of the aluminum methylene (AlCH2) free radical.

Extensive ab initio investigations of the ground and electronic excited states of the AlCH2 free radical have been carried out in order to predict the spectroscopic properties of this, as yet, undetected species. Difficulties with erratic predictions of the ground state vibrational frequencies, both in the literature and in the present work, have been traced to serious broken-symmetry instabilities in the unrestricted Hartree-Fock orbitals at the ground state equilibrium geometry. The use of restricted open-shell Hartree-Fock or complete active space self consistent field orbitals avoids these problems and leads to consistent and realistic sets of vibrational frequencies for the ground state. Using the internally contracted multireference configuration interaction method with aug-cc-pV(T+d)Z basis sets, we have calculated the geometries, energies, dipole moments, and vibrational frequencies of eight electronic states of AlCH2 and AlCD2. In addition, we have generated Franck-Condon simulations of the expected vibronic structure of the Ã-X̃, B̃-X̃, C̃-X̃, and C̃-Ã band systems, which will be useful in searches for the electronic spectra of the radical. We have also simulated the expected rotational structure of the 0-0 absorption bands of these transitions at modest resolution under supersonic expansion cooled conditions. Our conclusion is that if AlCH2 can be generated in sufficient concentrations in the gas phase, it is most likely detectable through the B̃2A2-X̃2B1 or C̃2A1-X̃2B1 electronic transitions at 515 nm and 372 nm, respectively. Both band systems have vibrational and rotational signatures, even at modest resolution, that are diagnostic of the aluminum methylene free radical.

Symmetry Breaking and Broken Ergodicity in Full Configuration Interaction Quantum Monte Carlo.

The initiator full configuration interaction quantum Monte Carlo method (i-FCIQMC) is applied to the binding curve of N2 in Slater-determinant Hilbert spaces formed of both canonical restricted Hartree-Fock (RHF) and symmetry-broken unrestricted Hartree-Fock (UHF) orbitals. By explicit calculation, we demonstrate that the technique yields the same total energy for both types of orbital but that as the bond is stretched, FCI expansions expressed in unrestricted orbitals are substantially more compact than their restricted counterparts and more compact than those expressed in split-localized orbitals. These unrestricted Hilbert spaces, however, become nonergodic toward the dissociation limit, and the total wave function may be thought of as the sum of two weakly coupled, spin-impure, functions whose energies are nonetheless very close to the exact energy. In this limit, it is a challenge for i-FCIQMC to resolve a spin-pure wave function. The use of unrestricted natural orbitals is a promising remedy for this problem, as their expansions are more strongly weighted toward lower excitations of the reference, and they provide stronger coupling to higher excitations than do UHF orbitals.

Perturbed atoms in molecules and solids: The PATMOS model

A new computational method for electronic-structure studies of molecules and solids is presented. The key element in the new model - denoted the perturbed atoms in molecules and solids model - is the concept of a perturbed atom in a complex. The basic approximation of the new model is unrestricted Hartree Fock (UHF). The UHF orbitals are localized by the Edmiston-Ruedenberg procedure. The perturbed atoms are defined by distributing the orbitals among the nuclei in such a way that the sum of the intra-atomic UHF energies has a minimum. Energy corrections with respect to the UHF energy, are calculated within the energy incremental scheme. The most important three- and four-electron corrections are selected by introducing a modified geminal approach. Test calculations are performed on N2, Li2, and parallel arrays of hydrogen atoms. The character of the perturbed atoms is illustrated by calculations on H2, CH4, and C6H6.

On the nature of electron correlation in C60

The ground state restricted Hartree Fock (RHF) wave function of C(60) is found to be unstable with respect to spin symmetry breaking, and further minimization leads to a significantly spin contaminated unrestricted Hartree Fock (UHF) solution (<S(2)> = 7.5, 9.6 for singlet and triplet, respectively). The nature of the symmetry breaking in C(60) relative to the radicaloid fullerene, C(36), is assessed by energy lowering of the UHF solution, <S(2)>, and the unpaired electron number. We conclude that the high value of each of these measures in C(60) is not attributable to strong correlation behavior as is the case for C(36). Instead, their origin is from the collective effect of relatively weak, global correlations present in the π space of both fullerenes. Second order perturbation (MP2) calculations of the singlet triplet gap are significantly more accurate with RHF orbitals than UHF orbitals, while orbital optimized opposite spin second order correlation (O2) performs even better.

Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

We present a group theoretical study of the symmetry-broken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N-electron single quantum dot (with and without an external magnetic field). The breaking of rotational symmetry results in canonical orbitals that (1) are associated with the eigenvectors of a H\"uckel Hamiltonian having sites at the positions determined by the equilibrium molecular configuration of the classical N-electron problem and (2) transform according to the irreducible representations of the point group specified by the discrete symmetries of this classical molecular configuration. Through restoration of the total-spin and rotational symmetries via post-Hartree-Fock projection techniques, we show that the point-group discrete symmetry of the unrestricted Hartree-Fock wave function underlies the appearance of magic angular momenta (familiar from exact-diagonalization studies) in the excitation spectra of the quantum dot. Furthermore, this two-step symmetry-breaking and symmetry-restoration method accurately describes the energy spectra associated with the magic angular momenta.

Theoretical study of the di-imide (N2H2) molecule in ground and n→π* excited states

A number of ab initio approaches have been used to determine the equilibrium structures, energies, and vibrational frequencies of N2H2 in the ground state and in the excited singlet and triplet n→π* states. The methods included restricted Hartree–Fock (RHF) and unrestricted Hartree–Fock (UHF), multiconfiguration self-consistent field (MCSCF), single-reference configuration interaction (SRCI) and multireference configuration interaction (MRCI) including all single and double excitations from the reference configurations, and second-order Mo/ller–Plesset perturbation theory (MP2) using RHF and UHF orbitals for ground and excited states, respectively. Unlike the singlet excited state, for which broken-symmetry solutions were found at the RHF level, no symmetry breaking was encountered for the triplet state. The ground-state MCSCF and MP2 structures of N2H2, which have C2h (trans-planar) symmetry, are in good agreement with the experimental structure. The excited states are predicted to have nonplanar C2 structures with dihedral angles ranging from 96° to 106° for the triplet state and from 105° to 121° for the singlet state. Except for the SRCI singlet adiabatic excitation energy, the effect of configuration interaction is to increase the vertical and adiabatic excitation energies of both excited states relative to the RHF values in single-reference calculations, and to decrease these excitation energies relative to MCSCF values in multireference calculations, bringing the single-reference and multireference CI values into better agreement with each other. The MRCI vertical excitation energies are 2.6 eV for the triplet and 3.6 eV for the singlet, while the corresponding 0–0 transition energies are 1.9 and 2.9 eV, respectively.

Construction of an effective hamiltonian for open‐shell molecular systems

AbstractAn effective Hamiltonian for open‐shell molecular systems is constructed. The unrestricted Hartree–Fock orbitals are applied as a basis set of one‐particle functions. This effective Hamiltonian is determined as a simple product of the original total Hamiltonian and the spin annihilator. The second‐quantization formalism and the Feynman–Goldstone diagrammatic technique are used. The resulting effective hamiltonian is composed of zero‐ to four‐particle terms. A possibility of applying the nondegenerate diagrammatic perturbation theory constructed over this effective Hamiltonian is discussed.

The effect of symmetry restrictions upon the hyperfine properties

The effect of spatial symmetry restrictions upon the calculated values of the hyperfine splitting constants is examined and results are reported for B, C, O and F. It is found that, if no symmetry restrictions are placed upon the unrestricted Hartree-Fock orbitals, the resulting hyperfine constants (except spin densities) are in good agreement with experiment and with configuration interaction calculations. Nuclear magnetic moments and quadrupole moments are reported on the basis of these calculations and the observed hyperfine structure.

A generalized mechanism for superexchange

The concepts of bond orbitals and unrestricted Hartree-Fock orbitals are used in an attempt to explain the mechanism of superexchange between magnetic cations via an intermediate anion. The resulting theory predicts the same results as the standard theories when the cation-anion-cation angle is 180°. For other values of this angle, however, the nature and strength of the interaction depends on the distribution of bonds round the anion and is not solely a function of angle. The theory is applied to compounds having the corundum-ilmenite and spinel structures, where it correlates the magnetic structures and transition temperatures for a number of compounds and enables these properties to be predicted for others.

On theZ-1/2expansion of unrestricted hartree-fock wave functions

It is pointed out that the perturbation expansions of unrestricted Hartree-Fock orbitals, based on zero-order uncorrelated orbitals, contain terms of order Z-1/2 which do not appear in the similar expansions of Hartree-Fock orbitals. It is shown that these terms give about 90% of the total radial correlation in the second-order energy of the 1S ground state of the two-electron systems.