Application of combined Hartree–Fock–Roothaan theory to molecules with arbitrary number of closed and open shells

In this study, the applicability of the combined Hartree–Fock–Roothaan (CHFR) theory of atomic-molecular and nuclear systems (Guseinov, J Math Chem 42:177, 2007) to the molecules is demonstrated using minimal basis set of Slater type orbitals (STO). As an example of application of CHFR theory, the calculations have been performed for the ground state of electronic configuration of methylene molecule CH ₂ which has two open shells. The results of computer calculations for the orbital, kinetic and total energies, linear combination coefficients of symmetrized molecular orbitals and virial ratios are presented.     

Is C4 bent?

Cheung and Graham have recently obtained high resolution ESR spectra of the C₄ molecule which show splittings of the perpendicular lines into separatex andy components [1]. Their interpretation of these new spectra is that triplet C₄ is not linear, but is slightly bent. This is contrary to numerous ab initio calculations. Using larger basis sets than have previously been employed for C₄, triple-zeta plus two sets of (d) polarization functions, denoted TZ (2d), and triple-zeta plus two sets ofd functions and one set off functions, denoted TZ (2df), the structure of this molecule has been reinvestigated via ab initio calculations which include electron correlation to second order in the many-body perturbation theory (MP2). Linear, several forms of alinear, and rhombic C₄ were studied. Within the levels of theory used here, triplet C₄ is found not to be bent, but rather is linear. The inclusion off functions in the basis set lowers the energy of rhombic C₄ over that of the linear isomer by about 10 kJ/mol.     

Use of unsymmetrical one-range addition theorems of Slater type orbitals in molecular electronic structure determination

In this work, the applicability of the unsymmetrical one-range addition theorems obtained from the use of complete orthonormal sets of Ψ^α-exponential type orbitals (Ψ^α-ETOs, where α = 1, 0, − 1, − 2, ...) to the study of electronic structure of molecules is demonstrated using minimal basis sets of Slater type orbitals (STOs). As an example of application of unsymmetrical one-range addition expansion method to evaluate the multicenter electronic integrals, the calculation has been performed for the ground state of BH ₃ molecule. The results of computer calculations for the orbital and total energies, and linear combination coefficients of symmetrized molecular orbitals are presented.     

AB initio SCF study of the electronic structure and spectrum of CuF2

MC SCF and contracted CI calculations have been performed for the three ligand-field states of CuF₂ and also for two charge-transfer states. With the most extensive basis set the calculated d-d transition energies, including a Davidson correctior for cluster effects, are 4150 cm^?1 (²11g) and 10560 cm^?1 (²Δg). These calculations were made with 98 basis functions, including of orbitals on Cu and d orbitals on F. To check the charge distribution in the molecule, calculations of the ESR g factors were also made at the SCF and CI levels of approximation. Resulting CI values are g_| = 1.93 (1.91) and g₁ = 2.76 (2.60). with corresponding experimental numbers in parentheses.     

MRD-CI calculations for the structure and stability of the hsin-hnsi isomers

Ab initio SCF and CI calculations are employed to determine the equilibrium geometrical parameters (bond lengths, stretching force constants and rotational constants B_e) for the two isomers HSiN and HNSi. It is found that HNSi is bound relative to H(²S) + SiN(²Σ⁺) by 122 kcal mole^?1, whereby the SiN(²π) state is predicted to lie only 13 kcal mole^?1 above SiN(²Σ⁺). The HNSi isomer is calculated to be more stable than HSiN by 68 kcal mole^?1 (CI treatment) and it is found that only a small barrier exists for angular inter-conversion between the two linear forms. A discussion of these results in the light of similar findings for other HAB systems containing first- and second-row atoms is presented Finally it is concluded on the basis of the present calculations that neither HNSi nor HSiN is a likely source for the observed interstellar molecular line U 81.5 (J = 2 → 1).     

Study of orbital transformation in configuration interaction calculations of hyperfine coupling in nitrogen and the CH molecule

Multi-reference configuration interaction calculations employing various orbital transformations are undertaken to obtain the isotropic hyperfine coupling constanta _iso in nitrogen anda _iso(H) in the CH molecule. The natural orbital (NO) basis is found to be more effective than the simple RHF-MO basis; the most obvious is a basis of spin natural orbitals (SNO). It is found thata _iso is approached from opposite sides in the NO and 2s shell SNO basis if the CI expansion is increased. Both results are within a few percent of the full CI limit for the nitrogen atom (in the given AO basis) and the experimental value for H in the CH radical. Various features of the SNO are discussed.     

The Rydberg states of trans-1,3-5-hexatriene from ab initio and configuration interaction calculations

Self-consistent ab initio and configuration interaction (CI) calculations are presented for the Rydberg states of the trans-1,3,5-hexatriene molecule. Seven Rydberg series were identified, four optically allowed (ns, nd _{s ²}, nd ₂₉) and three optically forbidden (np _z, np _y, np _z). These present results plus previous calculations on the valence states are used to assign the transitions observed in the ultraviolet (UV), electron-impact (EI) and two-photon spectra of this molecule.     

Configuration interaction calculations for the N2 molecule and its three lowest dissociation limits

A series of multi-reference double-excitation CI calculations is reported for the N₂ molecule in its equilibrium conformation as well as for its three lowest dissociation limits ⁴S + ⁴S, ⁴S + ²D and ⁴S + ²P respectively. Special emphasis is placed upon satisfying the requirement that the molecular CI energies at large internuclear separations must converge to the same values as are obtained in an analogous treatment for the corresponding atomic limits. In the most extensive CI undertaken the lowest three dissociation limits are calculated to occur at 9.33, 12.08 and 13.39 eV respectively compared to the experimental values of 9.90, 12.29 and 13.48 eV. The advantages of employing bond-centered functions in obtaining the proper balance between the bound molecule and its dissociated atoms are underscored in the calculations.     

Ab initio MRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. III. Me2N?NO2 decomposition of dimethylnitramine in a large crystalline environment

Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations, based on localized/local orbitals and an “effective” CI Hamiltonian, for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystalline or other solid environment. Our technique begins with an explicit quantum chemical SCF calculation for a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized, and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are then carried out for breaking a bond in the reference molecule. This method is completely general in that the space treated explicitly, as well as the surrounding space, may contain voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. Dimethylnitramine is the smallest prototype of the energetic R₂N—NO₂ nitramines, such as the 6-member ring RDX or the 8-member ring HMX. Decomposition of energetic compounds is initiated in the solid by a breaking of the target bond. Thus, it is crucial to know the difference in energy between breaking a bond in an isolated energetic molecule versus in the molecule in a solid. In the present study, we have carried out MRD-CI calculations for the Me₂N—NO₂ dissociation of dimethylnitramine in a dimethylnitramine crystal. The cases we investigated were one dimethylnitramine molecule (surrounded by 53 and 685 neighboring dimethylnitramine molecules represented by multipoles), three dimethylnitramine molecules, and three dimethylnitramine molecules (surrounded by 683 neighbors). All multipoles were cumulative atomic multipoles up through quadrupoles. The MRD-CI calculations on dimethylnitramine required large numbers of reference configurations from which were allowed all single and double excitations.     

Semi-empirical studies of torsional potentials in halonitrosomethanes

Semi-empirical molecular electronic structure calculations have been performed on a number of species of the general formulae CX₃NO and CX₂YNO, where X, Y = Cl, F and H. Potential energy curves for the internal rotation (torsion) of the nitroso functional group and geometric parameters of the molecules have been obtained. These calculations have employed the public domain AMPAC package, using both the MNDO and AM1 models available within that package. Graphical results are presented and compared with previous ab initio calculations and experimental determinations, where they exist. The results of these calculations should prove valuable as an aid in the analysis of the spectroscopy of these species.     

Complete TDA and RPA Calculations on the Electronic Transitions of Fullerene‐C60 in the CNDO/S and INDO/S Approximations*

Complete single‐excitation mixing calculations on the electronic transitions of the icosahedral C₆₀ molecule have been carried out with the Tamm–Dancoff approximation (TDA) and random‐phase approximation (RPA) schemes in the CNDO/S and INDO/S approximations. The complete space of 14,400 (1p–1h) pairs is partitioned into subspaces classified according to the irreducible representations of the Ih group. For this purpose, matrix representations of the group generators are obtained on a fixed set of basis functions and are used to construct the projection operators. Degenerate molecular orbitals in each energy level are symmetry‐adapted to these projection operators. Degenerate (1p–1h) pairs or singly excited configuration wave functions are similarly symmetrized. In addition, the Clebsch–Gordan coefficients are obtained and listed in an Appendix. The TDA and RPA equations are then solved for each irreducible representation separately. Both schemes with the projection operators and with the Clebsch–Gordan coefficients gave the same results as expected, indicating that the calculations were correctly done. The transition energies from the ground state 1¹A_g to low‐lying singlet and triplet excited states and the oscillator strengths for the allowed transitions (n¹T_1u–1¹A_g) are given in tables. A proper way to normalize is discussed for the eigenvectors of the RPA‐type matrix equation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

The Hylleraas-CI method in molecular calculations. III. Implementation and numerical verification of a three-electron many-center theory

The general theory of three-electron Hylleraas-Configuration-Interaction method using linear correlation factors of the form r_ij has been implemented for molecular systems using cartesian Gaussians as basis sets. A brief review of the theory and the form of the three-electron integrals is presented. Additionally, a table of numerical values of some selected three-electron integrals is given. Results from test calculations on H₃ using the full form of the theory are presented for some simple basis sets. A discussion of the computational problems that need to be overcome before this approach is competitive with traditional methods is included.     

The effect of bond functions on dissociation energies

The procedure employing bond functions recently suggested by Wright and Buenker has been applied to the N₂ X ¹Σ_g⁺ potential curve within the CAS SCF+MRSD Ci treatment of electron correlation. The basis set used herein is identical to that employed by these authors in their SCF+CI calculations. The D_e and the shape of the resulting potential curve, as judged by the computed vibrational levels, is not so accurate as would be expected from the results reported by Wright and Buenker. Our results indicate that using the CI superposition errors associated with bond functions to cancel basis set incompleteness depends on the treatment of the electron correlation.     

Molecular integrals in the generalized hylleraas–CI method

In the generalized Hylleraas–CI method, the original correlation factor r^v_ij is multiplied by a Gaussian geminal. Using the approach of generating functions, the general formulas of molecular integrals in this method are derived over Cartesian Gaussian orbitals. From differentiations of the generating functions, the expanding length in the incomplete Gamma functions is reduced, and some cancellations presented in other approaches are avoided. Preliminary calculations for H₂ and H₂—H₂ systems are carried out over STO -3G basis. The results are encouraging.     

Algorithm for variational calculations of molecular symmetry in solving anharmonic vibrational problems

A universal program for variational calculations of molecular symmetry in solving anharmonic vibrational problems, realized by the author, is described. The program uses the group-theoretical method. Symmetrized basis wave functions are constructed with the aid of the generalized KJebsch-Gordan series suggested by the author. The method of constructing symmetrized basis wave functions and the program for adequate calculations of molecular symmetry were verified for many molecules of different symmetry groups: O_h, O, T_d, T_h, T, D_∞h, C_t8v, D_nd, D_nh, D_n, C_nv, C_nh, S_2n, C_n, C_i, C_s, and C₁ where 2 ≤n ≤6. It was confirmed that the program provides correct results and high-speed operation. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 6, pp. 1146–1153, November–December, 1997.     

A preliminary ab initio investigation of the fate of the oxirane cation after vertical ionization of the oxirane molecule

A set of significant sections of the lowest energy hypersurfaces of the oxirane cation C₂H₄O⁺ are presented and discussed with the purpose of investigating the most probable rearrangement pathways following the initial ionization process. It is shown that the most important geometrical parameters involved in such processes are the ∠COC valence angle and the torsional angle of the two CH₂ groups. The most favoured rearrangement processes involve the second vertical ionization state from which it is possible to pass to a more stable open planar form via a conrotatory torsion of the two CH₂ groups and a moderate energy barrier. Other rearrangement processes involving a linear form are still possible. The calculations have been performed using a CI procedure starting from the molecular orbital space of the neutral parent molecule.     

Reliability of atomic natural orbital basis sets in calculations involving pseudopotentials

The performance of Atomic Natural Orbital (ANO) basis sets for calculations involving nonempirical core pseudopotentials has been studied by comparing the results for atomic and molecular nitrogen obtained using contracted ANO basis sets with those obtained using both the primitive set and a segmented one. The primitive set has been optimized at the SCF level for atomic N treated as a five-electron pseudo-atom, and consists of 7s and 7p primitive GTOs supplemented by 2d and 1f GTOs optimized at the CI level. From this primitive set three contracted [3s 3p 2d 1f] sets have been obtained. The first one has been derived from the ANOs of the neutral atom, the second has been obtained from an averaged density matrix and the third one is a segmented set. For the atom, the segmented set gives a zero contraction error at the SCF level as it must be in valence-only calculations. The ANO basis sets show some small contraction error at the SCF level but perform better in CI calculations. However, for the diatomic N₂ molecule the ANO basis sets exhibit a rather large contraction error in the calculated SCF energy. A detailed analysis of the origin of this error is reported, which shows that the conventional strategy used to derive ANO basis sets does not work very well when pseudopotentials are involved.