A derivation of the exact pi-electron hamiltonian

The exact pi-electron hamiltonian is derived from the full many-electron Schrödinger equation. The derivation employs techniques which also enable the development of open shell generalized perturbation theory. The parameters occurring in the pi-hamiltonian are therefore amenable to calculation using the approximate theories and methods of Sinano?lu, Nesbet, Kelly, etc. To a good approximation, the pi-hamiltonian is found to be generally consistent with its customarily assumed form.     

A second-quantization approach to the analytical evaluation of response properties for perturbation-dependent basis sets

A general theory for response properties is presented which is applicable to perturbations affecting the molecular basis set, notably nuclear derivatives. A perturbation-independent Fock space is introduced, and the necessary reorthonormalization of a truncated basis set after a perturbation is explicitly incorporated in the Hamiltonian. Explicit formulas for MCSCF first- and second-order properties are presented, and some computational aspects are briefly discussed. A brief comparison with previous results is given.     

A second-quantization framework for the unified treatment of relativistic and nonrelativistic molecular perturbations by response theory

A formalism is presented for the calculation of relativistic corrections to molecular electronic energies and properties. After a discussion of the Dirac and Breit equations and their first-order Foldy-Wouthuysen [Phys. Rev. 78, 29 (1950)] transformation, we construct a second-quantization electronic Hamiltonian, valid for all values of the fine-structure constant alpha. The resulting alpha-dependent Hamiltonian is then used to set up a perturbation theory in orders of alpha(2), using the general framework of time-independent response theory, in the same manner as for geometrical and magnetic perturbations. Explicit expressions are given to second order in alpha(2) for the Hartree-Fock model. However, since all relativistic considerations are contained in the alpha-dependent Hamiltonian operator rather than in the wave function, the same approach may be used for other wave-function models, following the general procedure of response theory. In particular, by constructing a variational Lagrangian using the alpha-dependent electronic Hamiltonian, relativistic corrections can be calculated for nonvariational methods as well.     

A new approach to the molecular rotational hamiltonian

The present paper is devoted to a new approach of the rotational hamiltonian of a non degenerate vibronic state of the semi-rigid molecules. It is based upon two points. Firstly the hermitian operators on a finiten dimensional vector space belong to an ² dimensional euclidian vector space. Secondly, the vector space of the rotational states is a direct sum of irreducible representations of the rotation group. Accordingly in each one of those representations the rotational hamiltonian can be represented by its set of real components on a orthonormal basis of hermitian operators. The components of the reduced hamiltonian of Watson limited to its quartic terms are determined.     

A note on the partitioning technique

A new derivation of the wave operator of the partitioning technique is given. Furthermore this approach is applied to derive wave operators for the inverse hamiltonian and in general for functions of the hamiltonian.     

Charge and spin correlation structures of conjugated π systems: Analysis of full CI wave functions of the PPP hamiltonian

An analysis of the electronic correlation structures by means of the charge and spin correlation functions is carried out for full CI wave functions of four, five, and six membered conjugated π systems described by the Pariser–Parr–Pople Hamiltonian. The low-lying states of these systems are classified as covalent (CV ) and ionic (IN ) states depending on whether the probability of finding two electrons simultaneously at the same position is small or large. It is found that many of excited CV states, the typical ones of which are the 2¹A_g state of linear π systems, have stronger CV character than the ground CV state, and their spin coupling structures are different from each other as well as from that of the ground CV state. The spin coupling structure in the ground CV state has an “antiferromagnetic” spin arrangement in favor of antiparallel coupling between nearest neighbor spins while in excited CV states the extent of the antiparallel spin coupling between nearest neighbor sites is decreased. IN states, which are less common for low-lying states than CV ones, are also found to have characteristic modulations in the charge correlation. In particular, the charge correlations in the lowest singlet IN states, 1¹B_u of linear π systems, 1¹B_2g of cyclobutadiene and 1¹B_1U of benzene, are alternating.     

One electron orbitals intrinsic to the reduced hamiltonian

One electron orbitals are determined from the reduced hamiltonian by a simple one-step diagonalization. These reduced hamiltonian orbitals (RHO's) are uniquely determined and virtual orbitals obtained in this procedure are on a par with filled orbitals. These RHO's appear well suited for CI calculations. Minimum basis set calculations are presented for H₂O and compared with similar SCF studies.     

Optimization of parameters for an effective hamiltonian

A generally applicable, least-squares method that can be used to optimize the parameters of an effective hamiltonian matrix in any basis set is described. The technique is applied to the correlation of photoelectron spectra of saturated hydrocarbons.     

A graphical symmetric group approach for a spin adapted full configuration interaction: partitioning of a configuration graph into sets of closed-shell and open-shell graphs

We developed a spin adapted full configuration interaction (FCI) method which was expected to be effective for parallel processing. The graphical symmetric group approach (GSGA) was employed, where a configuration graph was partitioned into several sets of closed-shell and open-shell graphs. The configuration state functions (CSFs) bearing the same number of closed-shells and open-shells were assembled in a configuration group. The graphical approach provided a number to identify each CSF in a sequential order within the group. Combination of this partitioning and an intermediate configuration-driven algorithm in calculating the so-called σ vectors allowed us to use symbolic coupling constants. Furthermore, this combination made it easy to implement an efficient algorithm suitable to task-distributed parallel procedure for evaluating σ vectors. A program was written and some test calculations were carried out with high parallel efficiency. The largest size of FCI used 10 million CSFs (20 million determinants).     

Some considerations on Ueff values entering the hubbard hamiltonian

One of the simplest ways to take into account correlations between electrons in solid state physics, beyond the usual one electron approximation, is to use the Hubbard Hamiltonian Although it corresponds to very severe approximations, since intersite correlations are neglected, and since the whole problem is reduced to a single parameter U, it is already very difficult to solve, and exact solutions exist in only a few cases. It is thus not desired to introduce more complications in the Hamiltonian; but it could be interesting to understand, at least qualitatively, which processes influence the value taken by parameter U. The question arises in concrete cases, such as transition metals or organic molecules; comparing experiments and approximate solutions of the Hubbard Hamiltonian has shown that, in most cases, the value of U that yields the best fit is very different from what would be expected from atomic considerations. For instance, if one wants to study correlations on atoms of type M, a pure atomic point of view would affect to U the change in energy U_at in the redox-type equation . However it seems that solid state effects play an important role and we discuss, in this paper, three of them: (i) the finite time that one electron spends on a given atom due to the delocalization of the electrons in a band (effect of β_ij which increases U relatively to U_at); (ii) the mixing of bands of different orbital character which allow two electrons not to be on the same orbital of an atom (and thus decreases U); and (iii) the existence of Coulomb repulsion between electrons on neighboring sites which reduces their effective exclusion on the same site.     

Modified one-electron hamiltonian method in the MC SCF theory

For orbital optimization within the MC SCF theory a modification of the OEH method is proposed with the direction of descent determined according to the Fletcher–Reeves gradient method. The combined method developed on this basis ensures the convergence of the iterative process when the Hessian singularities occur. The convergence properties of the method proposed are studied by performing the ab initio water molecule calculations using two types of multiconfigurational wave functions.     

A Hirshfeld partitioning of polarizabilities of water clusters

A new Hirshfeld partitioning of cluster polarizability into intrinsic polarizabilities and charge delocalization contributions is presented. For water clusters, density-functional theory calculations demonstrate that the total polarizability of a water molecule in a cluster depends upon the number and type of hydrogen bonds the molecule makes with its neighbors. The intrinsic contribution to the molecular polarizability is transferable between water molecules displaying the same H-bond scheme in clusters of different sizes, and geometries, while the charge delocalization contribution also depends on the cluster size. These results could be used to improve the existing force fields.     

Topological hamiltonian spectra of polycyclic benzenoid hydrocarbons

A general theory which points out the relations between Hückel-electron energy, the number of Kekulé structures and the HOMO-LUMO separation is presented. Some normalized topological invariants are derived from the concept of the spectral density function. A reasonably simple (three parameters) model spectral density function leads to universal relations between topological invariants that, although valid for any alternant molecule, were tested numerically for polycyclic benzenoid hydrocarbons. Some general conclusions concerning a distribution of the adjacency matrix eigenvalues are drawn.     

A numerical method to obtain a symmetry-adapted basis from the hamiltonian or a similar matrix

A practical method is proposed which using the hamiltonian matrix, or some other matrix corresponding to any operator with identical symmetry properties, enables one to obtain the transformation matrix, from the given basis to a symmetry-adapted basis. The method is very suitable for applications in the fields of molecular orbital and force constant calculations.     

Resonance by the complex coordinate method with hermitean hamiltonian

Using the complex coordinate method, a new hermitean hamiltonian is formulated, in which the resonance position and width are the “natural” perturbation strength parameters. If the resonance position is known the resonance width obtained by the presented theory is a lower bound to the exact value.