Ab initio studies on several species of the formula X3YO and X3YOH

Ab initio molecular orbital calculations using both minimal and extended basis sets have been applied to two isoelectronic sets of molecules. One set corresponds to the 18 electron species H₃NO, H₃CO^– and H₃COH while the second set contains the 42 electron fluorinated molecules F₃NO, F₃CO^– and F₃COH. The geometries of these molecules have been optimized, using both the minimal STO-3G and the extended 4-31G basis sets. These comparative calculations reveal that the 4-31G basis produced structural parameters in much better agreement with experiment. The effect of includingd-orbitals in the basis set was also investigated. For the fluorinated oxides it has been found that the optimized 4-31G structures were only slightly altered by the addition ofd-orbitals. For H₃NO, on the other hand, the inclusion ofd-orbitals considerably shortens the N-O bond distance. Both H₃NO and CF₃OH, which are unknown experimentally, are theoretically predicted to be capable of existence. The electronic structures of these molecules have also been examined using electronic partitioning according to the Mulliken scheme.     

Photoelectron Spectra of Azabenzenes and Azanaphthalenes: I. Pyridine,diazines, s-triazine and s-tetrazine

The experimental and theoretical basis of a recently proposed reassignment of the bands in the PE. spectra of pyridine, pyridazine, pyrimidine and pyrazine is discussed in detail. A characteristic feature of the derived orbital sequence is that it takes the ‘through-space’ and ‘through-bond’ interaction between the ‘lone pair’ basis orbitals explicitly into account. A simple parametrization of the orbital energies, based on HMO-type models for the π-orbitals and for the ‘lone pair’ linear combinations, yields excellent agreement with the observed band positions in the PE. spectra of s-triazine and s-tetrazine. Our new assignment is compared to those proposed previously.     

The excited states of pyrazine: A basis set study

Summary Multiconfigurational second order perturbation theory (CASSCF/CASPT2) has been used to investigate the dependence of computed valence excitation energies and transition moments on the basis sets. Pyrazine has been selected as the test molecule. Atomic normal orbital (ANO) type basis sets are used throughout. Contractions of the structure (4s3p1d/2s) are found to be an optimal compromise between the quality and the size of the calculations and are capable of yielding results virtually identical to more extended basis sets.     

Approximate valence-shell electron unrestricted Hartree-Fock calculations with orthogonalized atomic orbitals: Proton hyperfine splittings in benzyl and related radicals

A modified INDO procedure has been used to calculate the proton hyperfine splittings in benzyl and the isoelectronic anilino, phenoxy and 2-azabenzyl as well as 2- and 3-thenyl radicals. The present procedure differentiates between s-, p- and d-orbitals on an atom in estimating various integrals involving them, satisfies the rotational invariance requirements and employs an orthogonalized basis set of atomic orbitals for obtaining core-Hamiltonian matrix elements. The calculations based on using the exponents which depend only on the type of orbital and the nature of atom fail to provide correct relative order of ortho and para proton splittings in benzyl as well as anilino, phenoxy and 2-azabenzyl radicals. On the other hand, use of the exponents which are modified according to the charge densities in various orbitals leads to a high absolute value for para proton splitting compared to that for ortho proton splitting which in case of all these radicals is in agreement with experiment. A spin density calculation on benzyl, anilino and phenoxy radicals considering the variation of one-center one-electron and one-center two-electron integrals for different protons with their charges is found to yield further improvement in the relative order of ortho and para proton splittings in all these radicals. In 2- and 3-thenyl radicals the role of 3d-orbitals on sulfur has also been examined. To our knowledge, no unrestricted INDO calculations including 3d-orbitals on sulfur have been reported in the literature so far.     

Electronic States of 1,5-Cyclooctadiyne Radical Cation and of Related Systems: The electronic structure of cis-bent carbon-carbon triple bonds

The photoelectron spectra of 1,5-cyclooctadiyne ( 2 ) and of 1,6-dithiacyclodeca-3,8-diyne ( 3 ) have been recorded. The first four ( 2 ) or six ( 3 ) PE. bands have been assigned as follows; in increasing order of ionization potentials: The relative sequence and the positions of the PE. bands are explained in terms of through-bond and through-space interactions between the basis π-orbitals and σ-orbitals of appropriate symmetry behaviour. An analysis of the PE. spectroscopic data for cyclooctyne ( 1 ) and for ( 2 ) indicates that a cis-bend of the acetylene moiety by θ < 20° leads to a split in energy of the in-plane and out-of-plane basis π-orbitals which is smaller than ∽ 0.2 eV. This is in agreement with the predictions derived from semiempirical models (MINDO/2, SPINDO) and qualitative orbital arguments. However, it is shown by using orbital localization procedures, that the rationales underlying the two semiempirical models differ significantly.     

Molecular orbital energy levels for the sulfate Ion

A series of semiempirical molecular orbital calculations for the SO₄ ^2? ion is described. These calculations show the effect on the order of the molecular orbital energy levels of a) using the Wolfsberg-Helmholz approximation, b) using the Cusachs approximation, c) variation of the proportionality constant, F, in the Wolfsberg-Helmholz approximation, d) inclusion of d-orbitals in the basis set, and e) variation of ζ_d when d-orbitals are included. It is found that the highest filled level is t ₁ for all the Wolfsberg-Helmholz calculations when d-orbitals are included and is 3t ₂ for all the other calculations.     

Momentum space properties of various orbital basis sets used in quantum chemical calculations

Momentum expectation values (p^k), values of the momentum density P(p) at selected points, and coefficients in the MacLaurin and asymptotic expansions of P(p) are used to test the quality of various orbital basis sets previously used for the atomic helium Hartree-Fock problem. The wellknown position-space defects of Gaussian-type orbital expansions are shown to have their momentum-space counterparts. Expansions of even-tempered Slater-type orbitals are found to be rather accurate. The exponentially damped rational function is found to be the outstanding two-parameter unconventional orbital.     

Photoelectron-spectroscopic Evidence Concerning “Homo-aromaticity”

The first of the two π-bands in the photoelectron spectrum of cis-cis-cis-1, 4, 7-cyclononatriene (I, symmetry C_3v) shows a Jahn-Teller split. This is consistent with the prediction of molecular orbital theory that the top occupied orbitals of I are e (π) and a ₁(π) respectively. From the difference ?( e (π)) - ?( a ₁(π)) = 0.90 to 0.97 eV a value of β_1,3 = ?0.68 eV = 0.27 β (β = -2.5 eV) is obtained for the homoconjugative interaction of two π-orbitals in I. This value represents almost exclusively through-space interaction between the π-orbitals. Through-bond interaction (hyperconjugation) is a minor effect in I. A comparison of the photoelectron data of bicyclo [4.2.1] nonatriene with those of norbornene and cycloheptadiene shows that homoconjugation (homo-aromaticity) can only be detected by photoelectron spectroscopy if the interacting π-bonds (basis orbitals) are symmetry equivalent or have accidentally (almost) degenerate energies.     

Basis set quality. II. Information theoretic appraisal of various s- orbitals

The expectation values 〈r^k〉 (?2 ? k ? 4, k = 10), values of the charge density ρ(r) at selected points, and coefficients in the MacLaurin expansion of ρ(r) are used to test the quality of 71 orbital basis sets used for the atomic helium Hartree–Fock problem. These tests in position space are complementary to the momentum space tests previously carried out [Int. J. Quantum Chem. 21 , 419 (1982)]. Information theoretic measures with respect to either or both position and momentum space properties are subsequently defined and the orbitals are ranked accordingly. These measures indicate that, for a given orbital, momentum space properties are more poorly predicted than position space ones. Moreover an improvement in the virial ratio does not necessarily lead to a more balanced orbital with respect to position and momentum space properties. Basis sets containing Slater-type orbitals are again found to be rather accurate. The exponentially damped rational function is confirmed to be the outstanding two-parameter unconventional orbital.     

Consequences of Substitution in the Photoelectron Spectra of [2, 2]Paracyclophanes: Separation of ‘through-space’ and ‘through-bond’ interactions as a consequence of fluorosubstitution

The PE. spectra of [2, 2]paracyclophane ( 1 ), 4-amino[2, 2]paracyclophane ( 2 ) and 1, 1, 2, 2, 9, 9, 10, 10-octafluoro[2, 2]paracyclophane ( 3 ) are presented. The bands corresponding to ejection of the photoelectron from the five highest occupied π-orbitals have been assigned. The ‘observed’ orbital energies (i.e. the negative ionization potentials) are discussed in terms of ‘through space’ and ‘through-bond’ interactions between the semi-localized π-orbitals ( e_1g ) of the benzene moieties and the C, C-σ-orbitals of the ethylene bridges. The PE. spectrum of 3 shows that the fluorine-induced lowering of the C, C-σ-orbital energy effectively ‘turns-off’ the ‘through-bond’ interaction. The resulting pattern of the first four bands confirms the assignment given for 1 . Finally the band shifts induced by an amino group in position 4 are again in agreement with this assignment. Attention is drawn to the phenomenon of ‘orbital switching’ as a consequence of substitution in loosely coupled systems such as 1 .     

Approximate STO functions for the first-row transition metal atoms

Slater type orbital (STO) basis sets for the atoms Sc-Zn have been derived using a technique based on the distance between subspaces. The accuracy for several properties of these basis sets has been tested. Basis sets studied are of both single- and double-zeta sizes, although this technique can be generalized for any size. Uniform quality criteria through the series of atoms Sc-Zn are difficulty to establish due to the varying number of d electrons. A comparative study at the atomic level of the quality of STO basis sets (both the two new basis sets and Clementi's basis sets) for the first-row transition elements has been carried out. Results show that the new basis sets provide better simulation for several properties. Molecular calculations on compounds with these atoms using a Gaussian expansion fitted according to the new values of optimized STOs are also included. The results obtained are similar to those reported when STO-3G basis set is used.     

A systematic preparation of new contracted Gaussian-type orbital sets. VIII. MINI-1 and MIDI-1 sets for Ga through Cd

Minimal contracted Gaussian basis sets are presented for Ga through Cd. Characteristically these Gaussian-based minimal sets give far better d orbital energies than those by minimal STO basis sets. These new basis sets were tested on Br₂ for which a new benchmark calculation was also performed. The test result is satisfactory in that these basis sets produce good general agreement with the near Hartree–Fock calculation with respect to the molecular spectroscopic constants.     

Study of locally dense and locally saturated basis sets in localized molecular orbital calculations of nuclear shielding: Ab initio LORG calculations for 13C and 17O in norbornenone

This study demonstrates the use of uneven atomic basis sets for ab initio calculations of NMR shielding in the localized orbital/local origin (LORG) approach with norbornenone as the test case. We distinguish between locally dense sets (extended basis on target atom only) and locally saturated sets (extended bases on target atom and atoms in its first bonding sphere), using 6-311G ** and 6-31G sets to describe the high and low level of function sets. It is shown that the use of these uneven sets can simulate high basis set level calculations of shieldings for ¹H and for all the ¹³C nuclei in this molecule and, hence, allows quite accurate ab initio calculations of shielding properties of these nuclei in large molecules using relatively modest computational facilities. The shielding of the double-bonded ¹⁷O nucleus is apparently sensitive to basis-set quality beyond the first bonding sphere. © 1996 John Wiley & Sons, Inc.     

Bifunctional Hydrogen Bond Donor-Catalyzed Diels–Alder Reactions: Origin of Stereoselectivity and Rate Enhancement

The selectivity and rate enhancement of bifunctional hydrogen bond donor-catalyzed Diels–Alder reactions between cyclopentadiene and acrolein were quantum chemically studied using density functional theory in combination with coupled-cluster theory. (Thio)ureas render the studied Diels–Alder cycloaddition reactions exo selective and induce a significant acceleration of this process by lowering the reaction barrier by up to 7 kcal mol⁻¹. Our activation strain and Kohn–Sham molecular orbital analyses uncover that these organocatalysts enhance the Diels–Alder reactivity by reducing the Pauli repulsion between the closed-shell filled π-orbitals of the diene and dienophile, by polarizing the π-orbitals away from the reactive center and not by making the orbital interactions between the reactants stronger. In addition, we establish that the unprecedented exo selectivity of the hydrogen bond donor-catalyzed Diels–Alder reactions is directly related to the larger degree of asynchronicity along this reaction pathway, which is manifested in a relief of destabilizing activation strain and Pauli repulsion.     

A systematic preparation of new contracted Gaussian-type orbitals. IX [54/5], [64/5], [64/6], [74/6], [74/7] and MAXI-1–MAXI-5 from Li to Ne

The new contracted Gaussian-type orbitals (CGTO s) for molecular calculations have been developed from Li to Ne. The CGTO s are minimal type, i.e. composed of two s-type CGTO s, s₁, s₂, and one p-type CGTO , p₁. They are new family of CGTO s given by Tatewaki and Huzinaga, and others. In the previous works three primitive GTO s are used for s₂, which is the main part of the 2s orbital, whereas four primitive GTO s are employed in the present work. The sets generated are [54/5], [64/5], [64/6], [74/6], and [74/7]. In almost all the cases the errors in the 2s and 2p orbital energies are smaller than those of DZ . The resulting 2s orbitals are close to the orbitals of the uncontracted GTO sets, (13/n) and (14/n) of Duijneveldt. It is found that the 2s and 2p orbitals given by [64/6], [74/6], and [74/7] are satisfactorily near to those of Hartree–Fock. The basis sets [54/5], [64/6], and [74/7] are applied to the N₂ molecule in the split valence forms of [5211/311], [6211/3111], and [7211/4111]. Adding the d-type polarization functions from one through three, the quality of the basis sets has been examined. All of the three sets show good behavior and the sets augmented with three d-type polarization functions give almost entirely the same results as the very extended basis set.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Generally contracted basis sets for the first row transition metal atoms Sc-Zn have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over the three electronic configurationsd ⁿ ,d ^n–1 s, andd ^n–2 s ² for the neutral atom as well as the ground state for the cation and the ground state atom in an external electric field. The primitive sets are 21s15p10d6f4g. Contraction to 6s5p4d3f2g yields results that are virtually identical to those obtained with the corresponding uncontracted basis sets for the atomic properties, which they have been designed to reproduce. Slightly larger deviations are obtained with the 5s4p3d2f1g for the polarizability, while energetic properties still have only small errors. The design objective has been to describe the ionization potential, the polarizability and the valence spectrum as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations, which can be used together with basis sets of the same quality for the first and second row atoms.     

An ab initio molecular orbital study of structures and energies of spirocompounds: spiro[3.3]heptane and spiro[3.3]hepta-1,5-diene

Ab initio molecular orbital theory with the STO-3G and 4-31G basis sets is used to determine the equilibrium geometries, enthalpies of formation, strain energies and spiro-interactions for spiro[3.3]heptane and spiro[3.3]hepta -1,5 - diene. For spiro[3.3]heptane, molecular mechanics calculations suggest that the component cyclobutane rings are puckered to a greater extent than in cyclobutane itself. For spiro[3.3]hepta - 1,5 - diene, STO-3G calculations predict that the component cyclobutene rings deviate slightly from an orthogonal arrangement. Spiro-interactions in spiro[3.3]hepta - 1,5 - diene are revealed by comparing the calculated structural parameters and strain energies with those of appropriate reference systems. The π-orbitals in spiro[3.3]hepta -1,5 -diene are predicted to be split by about 0.4 eV.     

Spherically symmetric axial Gaussian lobe 3d and 4f orbitals

The axial Gaussian lobe orbital (AGLO ) representations of 3d and 4f orbitals proposed by LeRouzo and Silvi have been angularly optimized to ensure spherical symmetry of filled 3d and 4f shells. The functions have been tested on the hydrogen atom in the presence of high quality s and p basis sets and found to provide excellent minimal Gaussian representations of polarization functions. Exact orbital degeneracy is not obtained within each shell, however. Tabulated values are given to allow arbitrary scaling of the 3d and 4f lobe mimic orbitals.     

A systematic preparation of new contracted Gaussian-type orbital sets. III. Second-row atoms from Li through ne

Four minimal Gaussian basis sets are generated for the second-row atoms Li through Ne. The first one, MINI-1, consists of a 3-term contraction of primitive Gaussian-type orbitals for 1s, 2s, and 2p atomic orbitals. The convenient shorthand notation would be (3,3) for Li? Be and (3,3/3) for B? Ne. The second one, MINI-2, can be represented by (3,3/4) for B? Ne. In the same way, MINI-3 is described as (4,3) for Li? Be, and MINI-3 and MINI-4 are represented by (4,3/3) and (4,3/4) for B? Ne, respectively. Although the four basis sets are the minimal type, they give the valence shell orbital energies which are close to those of DZ. These four and other sets derived from them are tested for the hetero- and homodiatomic molecules and some organic molecules. They are found to give the orbital energies that agree well with those given by extended calculations. Atomization energies and other spectroscopic constants are also calculated and compared with those of extended calculations. The results clearly indicate that the present basis sets can be used very effectively in the molecular calculations.     

Basis set quality versus size II. Approximate GTO wave functions for second row transition metal atoms

Basis sets ranging in size from (16, 10, 7) to (20, 14, 11) have been derived for the atoms Y–Cd. Separate sets represent the energy optimized wave functions for each of the s²dⁿ, s¹dⁿ⁺¹, and s⁰dⁿ⁺² configurations. The energies from the largest sets are within 3 mhartrees of the values obtained in numerical Hartree–Fock calculations. Reasonable Hartree–Fock s²dⁿ– s¹dⁿ⁺¹ and s²dⁿ– s⁰dⁿ⁺² excitation energies may be obtained either using the largest basis sets, or using d-orbitals optimized for the s⁰dⁿ⁺² configurations. The basis sets are slightly unbalanced in favor of the s-functions and in disfavor of the d-functions, but various alternative basis sets may be derived by combining parts of the five parent sets. The convergence of radial expectation values is discussed.