Optimal group symmetric localized molecular orbitals

Summary The concept and generating method of optimum group symmetric localized molecular orbitals (OSLMOs) are proposed. The OSLMOs have strong points of orthogonality, equivalence and symmetry, and they are simultaneously as close to the classical VB structure as possible. By using the OSLMOs as one-electron orbitals the multiconfigurational correlation calculations are reduced. The scheme is also a valuable popularization and development to hybridization theory.     

Relativistic symmetry orbitals for the double groups C2v,C∞v,D∞h,and Oh

Relativistic symmetry orbitals are given for molecular LCAO calculations for the double groups: C_2v, C_∞v, D_∞h, and O_h (6-fold) coordination. The atomic orbitals used in the LCAO are of the four component form. A discussion of the comparison between nonre ativistic and relativistic molecular eigenvalues is presented.     

A group theoretical paradigm for describing the skeletal molecular orbitals of cluster compounds. Part 3

The group theoretical consequences of the Tensor Surface Harmonic Theory have been developed for [ML₂] _n , [ML₄] _n and [ML₅] _n clusters where either thexz andyz orx ²?y ² andxy components toL _d ^π andL _d ^δ do not contribute equally to the bonding. The closed shell requirements for such clusters are defined and the orbital symmetry constraints pertaining to the interconversion of conformers of these clusters are described.     

Relativistic double group spinor representations of nonrigid molecules

The character theory of relativistic double group spinor representations is developed in order to represent the total rovibronic states of nonrigid molecules. It is shown that the double groups can be represented in terms of wreath products and powerful matrix cycle type generators that are used to construct their character tables. It is shown that these tables are of use when spin-orbit coupling is included in the Hamiltonian even for molecules containing lighter atoms. Applications to nonrigid molecules such as Tl2H4/Tl2H4+ are considered. It is shown that the tunneling splittings and the nuclear spin statistical weights can be obtained for such species using the character tables thus constructed. The spinor double groups of several other molecules such as hexamethyl dilead and heavy weakly bound clusters such as (PoH2)4 are also considered.     

Localized molecular orbitals for polyatomic molecules

Molecular wavefunctions have been generated by the PRDDO (Partial Retention of Diatomic Differential Overlap) method for the monocyclic aromatic rings containing six π-electrons (C₄H ₄ ^?2 , C₅H ₅ ^? , C₆H₆, C₇H ₇ ⁺ , and C₈H ₈ ⁺² ) and ten π-electron species (C₈H ₈ ^?2 , C₉H ₉ ^? , C₁₀H₁₀). The eigenvalue spectra of the canonical molecular orbitals are presented. Localized molecular orbitals (LMO's) generated using the Boys criterion are reported for localizations involving all occupied molecular orbitals (complete localizations) and localizations of the π orbitals only. We find evidence for σ-π separation in the complete localizations for some of these molecules even though the Boys criterion is often biased against such results. We demonstrate for C₆H₆ and find for the other molecules that the π-orbital localizations are indeterminate (i.e. there are an infinite number of equally satisfactory LMO structures between two limiting extremes). This result may be viewed as a corollary of Hückel's (4n+2) rule for aromaticity.     

Hybrid molecular orbitals for reacting systems

A method of describing the interactions between two systems in terms of coupled hybrid molecular orbitals of fragments is discussed and is applied to simple interacting systems to provide information on the processes of bond formation.     

Localized molecular orbitals for aromatic molecules

Localized molecular orbitals are calculated using the method of Boys for the aromatic molecules C₆H₆, C₆H₅X and the p-, m-, and o-forms of C₆H₄XY, where X,Y = CN,OH,F. The calculations are performed both with and without the constraint of σ, π-separation in the localization. The localized π-orbitals are multicenter bonds. If the σ- and π-orbitals are localized together, two different structures are found, Kekulé-type structures and structures with a set of six two center and a set of three three center bonds. The C-X bond turns out to be a single bond if X = CN and a double bond, if X = OH or F.     

Localized orbitals for the description of molecular interaction

The intermolecular interaction between the molecules CH₂O and NH₃ was investigated by the supermolecule method. The interaction energies were first calculated at the ab initio SCF level, and the electron correlation was included via second-order Møller-Plesset perturbation theory (MP 2). The basis set superposition error (BSSE ) was taken into account by the counter-poise (CP ) method. The occupied and the virtual canonical molecular orbitals (CMOS ) of the supermolecule were separately localized by the Boys' procedure. The correlation correction was calculated by the many-body perturbation theory (MBPT ) in the localized representation. Contributions of the third- and fourth-order localized diagrams were added to those of the second-order canonical diagram. This procedure gives a correction nearly equivalent to that of MP 2. The possibility to separate LMO contributions responsible for the dispersion interaction was investigated.     

Localized orbitals for optimal decomposition of molecular properties

We present the procedure for transforming delocalized molecular orbitals into the localized property-optimized orbitals (LPOs) designed for building the most accurate, in the Frobenius norm sense, approximation to the first-order reduced density matrix in form of the sum of localized monoatomic and diatomic terms. In this way, a decomposition of molecular properties into contributions associated with individual atoms and the pairs of atoms is obtained with the a priori known upper bound for the decomposition accuracy. Additional algorithm is proposed for obtaining the set of “the Chemist's LPOs” (CLPOs) containing a single localized orbital, with nearly double occupancy, per a pair of electrons. CLPOs form an idealized Lewis structure optimized for the closest possible reproduction of one-electron properties derived from the original many-electron wavefunction. The computational algorithms for constructing LPOs and CLPOs from a general wavefunction are presented and their implementation within the open-source freeware program JANPA ( http://janpa.sourceforge.net /) is discussed. The performance of the proposed procedures is assessed using the test set of density matrices of 33 432 small molecules obtained at both Hartree-Fock and second-order Moller-Plesset theory levels and excellent agreement with the chemist's Lewis-structure picture is found.     

Reference program for molecular calculations with Slater-type orbitals

A program for computing all the integrals appearing in molecular calculation with Slater-type orbitals is reported. The program is mainly intended as a reference for testing and comparing other algorithms and techniques. An analysis of the performance of the program is presented, paying special attention to the computational cost and the accuracy of the results. Results are also compared with others obtained with Gaussian basis sets of similar quality. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1284–1293, 1998     

On the defects of molecular symmetry-lobe orbitals

It is proved that two molecular symmetry-lobe orbitals, belonging to different irreducible representations, can have a non-negligible overlap. Using a previously reported multipolar analysis of Gaussian-lobe orbitals (GLOs), it is demonstrated that such defects occur when individual symmetry orbitals (SOs) are both contaminated in a given Y_1m subspace, even if such contaminations are very small. A numerical application illustrates this result in the case of the NH₃ molecule, and it is shown that axial-GLOs allow for the exact cancellation of the symmetry defects.     

An efficient method for constructing nonorthogonal localized molecular orbitals

A new method for constructing nonorthogonal localized molecular orbitals (NOLMOs) is presented. The set of highly localized NOLMOs is obtained by minimization of the spread functional starting from an initial set of canonical orthogonal molecular orbitals. To enhance the stability and efficiency, the centroids of the NOLMOs are constrained to be those of the corresponding orthogonal localized molecular orbitals (OLMOs), which are obtained with the Boys criterion in advance. In particular, these centroid constraints make the optimization for each NOLMO independent of the others, which is an attractive feature for application to large systems. The minimization with the constraints incorporated through the multiplier-penalty function method is stable and efficient in convergence. While exhibiting the classical bonding pattern in chemistry and sharing a spatial distribution similar to that of the corresponding OLMOs, the obtained NOLMOs are more compact than the corresponding OLMOs with about 10%-28% reduction in the value of the spread functional and devoid of the troublesome "orthogonalization tails."     

On the use of local basis sets for localized molecular orbitals

Two procedures are discussed for the direct variational optimization of localized molecular orbitals which are expanded in local subsets of the molecular basis set. It is shown that a Newton-Raphson approach is more efficient than an iterative diagonalization scheme. The effect of the basis-set truncation on the quality ofab-initio SCF results is investigated for Be, Li₂, HF, H₂O, NH₃, CH₄ and C₂H₆.     

The optimization of molecular orbitals for coupled cluster wavefunctions

The purpose of this work is to make the coupled cluster (CC) energy stationary with respect to molecular-orbital (MO) variations in the reference configuration. To achieve this, we have used the Z vector, the solution of a set of perturbation-independent CPHF-like equations, to rotate the MOs. A new energy and gradient calculation is carried out with these non-SCF orbitals to obtain a new Z vector. The process is repeated until the orbitals are optimized (Z = 0), i.e. the contribution to the analytic CC gradient coming from orbital relaxation (CPHF) is zero. At the CCD level the orbitals thus obtained are approximate Brueckner orbitals. At the CCSD level, convergence problems were found in the iterative procedure to optimize the orbitals. Results obtained for several molecules show that CCD wavefunctions constructed from these optimized orbitals are of CCSD quality. We conclude that the presence of exp(t₁) in the CCSD model accounts for most relaxation effects and there is not much to gain by orbital optimization in CCSD wavefunctions.     

An analysis of the complex molecular orbitals method

Numerical results for the ground state of the HN ₂ ⁺ and HCO⁺ molecular ions at their near equilibrium geometry, obtained by the complex molecular orbitals (CMO) method in the extended basis set, are reported. The CMO wavefunction of the HN ₂ ⁺ ion is compared with the CI wavefunction obtained in the same basis set. This reveals the nature of approximations inherent in the CMO method. A peculiar feature of the occupation numbers of the CMO natural orbitals is also explained.Alexander von Humboldt Fellow. On leave from the Institute Rudjer Bokovi, Zagreb, Croatia, Yugoslavia.