Compact basis sets for LCAO-LSD calculations. Part II: Tests for Cr2 and Ni4

The compact orbital and auxiliary basis sets for LCAO-LSD calculations introduced in Part I are tested in molecular calculations on Cr₂ and Ni₄. The present results for spectroscopic constants and valence orbital energies obtained using medium size orbital expansions with a double-zeta representation for valence orbitals are in very good agreement with those previously calculated with very extended sets. Since the computational time of the present calculations is reduced severalfold compared with the extended basis set calculations, the present basis sets allow increased efficiency of the LCAO-LSD calculations and allow the method to be extended to larger systems.     

Ab initio calculations,using a small Gaussian basis set,of the electronic structure of the sulphate ion

Ab initio molecular orbital calculations of the electronic structure of the sulphate ion have been performed in which three Gaussian-type functions are used to simulate each member of a minimal basis of Slater-type orbitals. Comparative calculations on H₂S show that such a basis excellently reproduces the properties of the valence electrons given by calculations in a Slater basis. The expansion of the basis by the addition of sulphur 3d orbitals results in a large decrease in the molecular energy (1 a.u.) and has a pronounced effect on the ordering and energy of the molecular orbitals. The results of a number of semiempirical schemes are discussed in the light of these results.     

Approximate molecular orbital theory: the ese mo formalism. II. Direct comparison with ab initio results

The utility of the ESE MO formalism is examined in relation to ab initio results, when a typical small gaussian basis is employed. Good electronic structure predictions result from simplified schemes based on the ESE MO formalism, despite adverse features of the chosen basis set, for the diverse group of molecules FH, OH₂, NH₃, FCN, O₃ and OF₂.     

An approximate frozen core approach to valence only molecular calculations

A simple valence electron-only theory based on an approximate frozen core approach and an exact core-valence strong orthogonality condition is developed for atomic and molecular systems. A unique reduced basis is introduced in which both core and valence orbitals are expanded. The core representation is roughly approximated, and the valence orbital overlap with the corresponding all-electron reference functions is nearly exact. The size of the reduced basis in terms of primitive functions is practically the same as that adopted by effective core potential methods in which the valence orbitals have the correct nodal properties. Results obtained with the present approach are presented for LiO, BeO and CaO molecules, and compared with the corresponding all-electron frozen core calculations. In addition, a detailed investigation on Li _n Be clusters (n=1,..., 6) is carried out.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Comparison of valence-only model potential and all-electron ab initio LCAO SCF MO studies of Li2 and LiH

A previously developed gaussian-based model potential theory for a single valence electron outside a core has been extended to the simple two-valence electron systems Li₂ and LiH within the LCAO SCF MO formulation, using an extended valence basis set. Comparisons of the results with corresponding ab initio calculations show excellent agreement of the total valence energy and the orbital energy in both systems, and for the dipole moment in LiH.     

One-center expansion method with model potentials. I. Formulation and test calculations

The one-center expansion (OCE ) method is extended to evaluate molecular wave functions for molecules with heavy off-center nuclei. This extension is achieved through the use of model potentials (MP ) to approximate the highly bound core orbitals. The remaining diffuse valence charge distribution is then rather easy to simulate using OCE . The formulation of the method is described. New molecular integrals are solved to a high degree of accuracy. Successful results are reported for H₂O, H₂S, and N₂. The valence electron distributions and orbital energies are in good agreement with those obtained from more complete calculations. The method combines the computational economy of both OCE and MP procedures, resulting in a potentially useful package for further chemical applications.     

Ground electronic state and geometry of SF3

Ab initio LCAO MO SCF calculations with DZ + 3d(S) basis functions show that the sulphur trifluoride radical is a planar π-radical having a ²B₁ ground state. Like ClF₃, it has an umbrella-structure. However, it becomes Y-shaped in its first ²A₁ excited state which has been calculated to lie only ≈ 2.4 eV above the ²B₁ ground state.     

The nature of the chemical bond in UO2

The nature of the chemical bond in UO₂ was analyzed taking into account the X-ray photoelectron spectroscopy (XPS) structure parameters of the valence and core electrons, as well as the relativistic discrete variation electronic structure calculation results for this oxide. The ionic/covalent nature of the chemical bond was determined for the UO₈ (D_4h) cluster, reflecting uranium's close environment in UO₂, and the U₁₃O₅₆ and U₆₃O₂₁₆ clusters, reflecting the bulk of solid uranium dioxide. The bar graph of the theoretical valence band (from 0 to ~35 eV) of XPS spectrum was built such that it was in satisfactory agreement with the experimental spectrum of a UO₂ single crystalline thin film. It was shown that unlike the crystal field theory results, the covalence effects in UO₂ are significant due to the strong overlap of the U 6p and U 5f atomic orbitals with the ligand orbitals, in addition to the U 6d atomic orbital (AO). A quantitative molecular orbital (MO) scheme for UO₂ was built. The contribution of the MO electrons to the chemical bond covalence component was evaluated on the basis of the bond population values. It was found that the electrons of inner valence molecular orbitals (IVMO) weaken the chemical bond formed by the electrons of outer valence molecular orbitals (OVMO) by 32% in UO₈ and by 25% in U₆₃O₂₁₆.     

Applications of ESCA to polymer chemistry. X. Core and valence energy levels of a series of polyacrylates

The core and valence levels of a series of poly(alkyl acrylates) have been studied by ESCA. From an analysis of the individual component peaks for the C_1s and O_1s core levels and from comparison of relative area ratios it is shown that ESCA may be applied to the study of surface compositions. The evidence presented strongly suggests that on the ESCA depth-profiling scale the technique statistically sample the repeat units with no evidence for preferential orientation of side chains at the surface. For some samples, ESCA provides evidence for a degree of surface oxidation and hydrocarbon contamination. The valence energy levels are shown to be characteristic of the polymer system. The measured absolute and relative binding energies of the core levels have been compared with model calculations using the charge-potential model in the CNDO/2 SCF MO formalism.     

On the adequacy of the molecular-orbital picture for describing ionization processes

General arguments concerning the adequacy of the molecular-orbital (MO ) ionization picture are given. Whereas the MO ionization picture is found to be valid for both outer valence and core electrons, it may completely break down in the inner valence region. The general considerations are supported by many-body calculations on methane, acetylene, hydrogen cyanide, and dinitrogen tetroxide. It is demonstrated that the breakdown of the MO ionization picture is a common phenomenon.     

Fully relativistic calculations of ThF4

Based on the results of first‐principles density functional theory calculations of the electronic structure of ThF₄ in solid state and molecular form, the study of the Th6p, 5f, 6d, 7s and F2s, 2p states was done. We used the fully relativistic cluster discrete variational method with the local exchange‐correlation potential. The hybridization of F2p and Th5f, 6d, 7s, 7p states in the valence molecular orbitals (VMOs) in the region 0–10 eV and of F2s and Th6p states in the inner valence molecular orbitals (IVMOs) in the region 10–50 eV was studied. The results of relativistic cluster calculations are compared with those obtained for ThF₄ molecule. The energies of ionization of VMOs and of IVMOs were evaluated on the basis of the ground‐state and Slater's transition‐state calculations. The MO energy levels provide a satisfactory interpretation of experimental photoelectron spectra. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Optimized Slater-type basis sets for the elements 1-118

Seven different types of Slater type basis sets for the elements H (Z = 1) up to E118 (Z = 118), ranging from a double zeta valence quality up to a quadruple zeta valence quality, are tested in their performance in neutral atomic and diatomic oxide calculations. The exponents of the Slater type functions are optimized for the use in (scalar relativistic) zeroth-order regular approximated (ZORA) equations. Atomic tests reveal that, on average, the absolute basis set error of 0.03 kcal/mol in the density functional calculation of the valence spinor energies of the neutral atoms with the largest all electron basis set of quadruple zeta quality is lower than the average absolute difference of 0.16 kcal/mol in these valence spinor energies if one compares the results of ZORA equation with those of the fully relativistic Dirac equation. This average absolute basis set error increases to about 1 kcal/mol for the all electron basis sets of triple zeta valence quality, and to approximately 4 kcal/mol for the all electron basis sets of double zeta quality. The molecular tests reveal that, on average, the calculated atomization energies of 118 neutral diatomic oxides MO, where the nuclear charge Z of M ranges from Z = 1-118, with the all electron basis sets of triple zeta quality with two polarization functions added are within 1-2 kcal/mol of the benchmark results with the much larger all electron basis sets, which are of quadruple zeta valence quality with four polarization functions added. The accuracy is reduced to about 4-5 kcal/mol if only one polarization function is used in the triple zeta basis sets, and further reduced to approximately 20 kcal/mol if the all electron basis sets of double zeta quality are used. The inclusion of g-type STOs to the large benchmark basis sets had an effect of less than 1 kcal/mol in the calculation of the atomization energies of the group 2 and group 14 diatomic oxides. The basis sets that are optimized for calculations using the frozen core approximation (frozen core basis sets) have a restricted basis set in the core region compared to the all electron basis sets. On average, the use of these frozen core basis sets give atomic basis set errors that are approximately twice as large as the corresponding all electron basis set errors and molecular atomization energies that are close to the corresponding all electron results. Only if spin-orbit coupling is included in the frozen core calculations larger errors are found, especially for the heavier elements, due to the additional approximation that is made that the basis functions are orthogonalized on scalar relativistic core orbitals.     

SCF-Xα MO studies of the x-ray spectra of CuO and ZnO

SCF-Xα scattered wave cluster MO calculations for the oxyanions CuO^?6₄ (D_4h symmetry) and ZnO^?6₄ (Td symmetry) yield results in good agreement with the X-ray photoelectron and X-ray emission spectra of CuO and ZnO, respectively. Agreement of the calculations with optical data is fair. Calculations of the valence electron and core electron hole states of these oxyanions support the assignment of photoelectron shakeup satellites to valence band to conduction band transitions. Calculated shakeup energies for the Cu2p core spectrum in CuO are 7.4 and 9.9 eV (cf. experimental values of 7.5 and 10.0 eV) while shakeup peaks in the valence region spectrum are predicted at 6.1 and 8.0 eV. (Cf. a broad peak with maximum at 8.1 eV observed experimentally.) The absence of intense low energy satellites in the spectra of ZnO is explained by the small amount of electron reorganization in the outer valence levels attendant upon hole formation.     

Nonempirical ab initio studies on inner-sphere reorganization energies of M2+(H2O)6/M3+(H2O)6 redox couples at valence basis level

On the basis of the basic feature of the electron transfer reactions, a new theoretical scheme and application of a nonempirical ab initio method in computing the inner-sphere reorganization energies (RE) of hydrated ions in electron transfer processes in solution are presented at valence STO basis (VSTO) level. The potential energy surfaces and the various molecular structural parameters for transition metal complexes are obtained using nonempirical molecular orbital (MO) calculations, and the results agree very well with experimentally observed ones from vibrational spectroscopic data. The results of inner-sphere REs obtained from these calculations via this new scheme give a good agreement with photoemission experimental findings and those from the improved self-exchange model proposed early for M²⁺(H₂O)₆/M³⁺(H₂O)₆(M = V, Cr, Mn, Fe, and Co) redox couple systems and are better than those from semiempirical INDO/II MO method and other classical methods. Further, the observed agreement of the optimized structural data and the results of inner-sphere REs of complexes with experimental findings confirms the following: (1) the validity of nonempirical MO calculation method to get accurate structural parameters and inner-sphere RE for the redox systems for which reliable vibrational spectroscopic data are not available, (2) the validity of the improved self-exchange model proposed early for inner-sphere RE, and (3) the reasonableness of some approximations adopted in this study. © 1997 John Wiley & Sons, Inc.     

Proton n.m.r. spectra of furo[3,2-c] and furo[2,3-c]thiapyrylium cations,compared with their thieno homologues. Correlations between chemical shifts and charge densities from CNDO/2 and PPP calculations

Significant variations of thiapyrylium chemical shifts, by comparison with their thienohomologues, are shown by ¹H n.m.r. spectra of furo[3,2-c]thiapyrylium and furo[2,3-c]thiapyrylium perchlorates. The observed changes can be ascribed to a different distribution of the electron charge (mainly caused by participation of the 3d orbitals of sulphur in the thienohomologues) and to a different contribution of the ring current; this is shown by MO calculations performed by the CNDO/2 and the coupled Hartree–Fock methods, respectively.     

Exponential transformation of molecular orbitals. II. General formulation for UHF calculations and application to diatomics and molecular fragments

The exponential transformation of the molecular orbitals, that has been previously used to achieve a process with a convergence of quadratic quality in SCF closed-shell calculations [J. Chem. Phys. 72 , 1452 (1980)] has been extended to UHF determinantal wave functions built from different orbitals for different spins. Explicit formulas are given for the first and second derivatives of the energy to be varied. The method is illustrated by UHF calculations for systems described as standard singlets (Li₂ and F₂) or triplets (NH) at the RHF approximation level, as well as for CH, CH₂, CH₃ molecular fragments in their valence states.     

Contracted Gaussian-type basis functions revisited. IV. Atoms Rb to Xe

We report minimal-type contracted Gaussian-type function (GTF) sets, #n=(n3333/n33/n3) with n=5 and 6, #7= (74333/743/74), and #8= (84333/843/75), for the fourth-row atoms from Rb to Xe. Test calculations are performed on the Ag₂ molecule. Spectroscopic constants given by split valence sets derived from #5 and #6 are a little contaminated by basis set superposition error. However, we find that the fully valence split #8 set, (8433111/84111/711111), yields essentially the same results as a large GTF set, (22s15p12d), with a general contraction, when p-, d-, and f-type polarization functions are augmented. The present #7 and #8 CGTF sets are recommended for ab initio molecular calculations including fourth-row atoms. Received: 15 January 2002 / Accepted: 16 April 2002 / Published online: 24 June 2002