Extended Koopmans' theorem: Approximate ionization energies from MCSCF wave functions

The extended Koopmans' theorem has been implemented using multiconfigurational self-consistent field wave functions calculated with the GAMESS, HONDO, and SIRIUS programs. The results of illustrative calculations are presented for the molecules HF, H₂O, NH₃, CH₄, N₂, CO, HNC, HCN, C₂H₂, H₂CO, and B₂H₆. The lowest extended Koopmans' theorem ionization potentials agree well within the experimental values and the ionization potentials representing excited states of the ions show some improvements over the Koopmans' theorem values in most cases. The extended Koopmans' theorem is easily implemented and the time required to calculate the ionization energies is insignificant compared to the time required to calculate the wave function of the un-ionized molecule. © 1992 by John Wiley & Sons, Inc.     

ESCA applied to polymers. XXVI. Investigation of a series of aliphatic,aromatic, and fluorine-containing polycarbonates

The absolute and relative binding energies for the C_1s, O_1s, and F_1s core levels have been determined using x-ray photoelectron spectroscopy (ESCA) for a series of aliphatic, aromatic, and fluorine-containing polycarbonates. Comparisons of these experimentally determined, core-level binding energies with theoretical calculations using the ground-state potential model in the CNDO/2 SCF MO formalism as well as model compounds have been made on the C_1s and O_1s core levels. The degree of polymerization for low-molecular-weight fluorine-containing polycarbonates, as determined from ESCA measurements, is compared to measurements by vapor-phase osmometry and ¹⁹F-NMR.     

Applications of ESCA to polymer chemistry. XVII. Systematic investigation of the core levels of simple homopolymers

The core levels of a series of 83 homopolymers have been studied by electron spectroscopy for chemical analysis (ESCA). Comparisons of the experimentally determined core-level binding energies with theoretical calculations using the ground-state potential model in the complete neglect of differential overlap (CNDO/2) self-consistent field molecular orbital (SCF MO) formalism have been made on the C_1s and O_1s core levels for the oxygen-containing polymers in the series. A comparison of the ground-state potential model (GPM) and relaxation potential model (RPM) on a series of six model compounds representative on the series of polymers is given. Compilations are given of binding energies of C_1s, O_1s, N_1s, Cl_2p, S_2p, Si_2p, and Br_3d levels for typical structural features of common occurrence in polymer systems. These data, taken in conjunction with that previously published on fluoropolymers, provide a sound basis for the development of ESCA as a fingerprint tool in the elaboration of features of structure and bonding in polymers in general.     

A theoretical investigation of molecular core binding and relaxation energies in a series of oxygen-containing organic molecules of interest in the study of surface oxidation of polymers

Nonempirical LCAO MO SCF computations (in the ΔSCF formalism) have been carried out of binding energies and relaxation energies for an extensive series of oxygen-containing organic systems encompassing most of the common functionalities. The molecules for which experimental data are available for comparison demonstrate the adequacy of the treatment for describing the relative binding energies for both the C_ls and O_ls core levels. A sound basis is therefore provided for the discussion of relative core binding energies (C_ls and O_ls) for functionalities for which experimental data are not available, that is, hydroperoxides, peroxides, peroxyacids, and peroxyesters, a knowledge of which is essential for investigations of the surface oxidation of polymers by means of ESCA. C_ls shifts are discussed in terms of primary and secondary substituent effects of oxygen, which greatly simplify the analysis of complex unresolved spectra, whereas for the O_ls levels a similar but less straightforward situation exists. The relaxation energies associated with both C_ls and O_ls core ionization follow a dependence on the binding energy for a given structural type.     

Hartree-Fock calculations and photoelectron spectra of SSO and NSF

Results from ab initio Hartree-Fock calculations on the ground states of SSO and NSF are reported. The calculations employ large basis sets of Gaussian functions of essentially double zeta quality. The photoelectron spectra of the bent triatomic molecules with 18 valence electrons, i.e. SSO, NSF, O₃, SO₂, NSCl are compared. Further experimental details of the photoelectron spectrum of SSO are presented and an assignment of the observed ionic states of SSO⊕ is attempted. The calculated dissociation energies, dipole moments and the population analyses are given. The correlation effect is qualitatively discussed in connection with the applicability of Koopmans' theorem for the bent tri-atomic molecules.     

Some theoretical aspects of vibrational fine structure accompanying core ionizations in N2 and CO

Ab initio calculations have been carried out on CO and N₂ and the relevant core hole states with different basis sets to investigate differences in geometries and force constants. From these calculations vibrational band profiles of the core level ESCA spectra for these molecules have been interpreted, obviating the need to rely on data pertaining to the equivalent core species. The agreement with experimental profiles is excellent. The O_1s level of CO which has not been subjected to detailed theoretical analysis previously, is predicted to show substantial vibrational structure in excellent agreement with recently acquired experimental data. The effect of temperature on the band profiles has also been considered. Theoretically derived core binding and relaxation energies of these systems have been investigated both as a function of basis set, and of internuclear distance. Density difference contours have been computed and give a straightforward pictorial representation of the substantial electron reorganizations accompanying core ionizations. Small basis sets with valence exponents appropriate to the equivalent core species when used in hole state calculations describe bond lengths, force constants, core binding energies and relaxation energies with an accuracy comparable to that appropriate to the corresponding extended basis set calculations.     

A non-empirical LCAO MO SCF investigation of electronic relaxations accompanying core ionizations in the series X2 and HX (X = F, Cl and Br)

A theoretical analysis has been made of differences in relaxation energies for photoionization from the core levels of the series X₂, HX for X = F, Cl, Br. It is demonstrated that whilst the charge in relaxation energies is largest for F₂ with respect to HF, the contribution to the shifts in core levels is relatively larger for the series X₂ and HX for X = Cl, Br. It is further shown that shifts in binding and relaxation energies show very little dependence on the core levels studied.     

Ab initio calculations on furan with a new computer program

Two ab initio calculations with different basis sets have been performed on the molecule furan, C₄H₄O. The calculations were done with a new computer program, REFLECT, which is presented. A preliminary analysis of the molecular wave functions has been made by looking at total and orbital energies and also by means of a population analysis. One inner shell ionization energy has been calculated by taking the difference in total energy for the molecule and the corresponding ion. The result is compared with the ionization energy obtained from Koopmans' theorem.     

Oxygen-induced next-nearest neighbour effects on the C1s-levels in polymer XPS-spectra

This letter reports the results of ab initio quantum chemical calculations on the C_1s core levels of model systems for a number of oxygen containing polymers. Conformational effects were studied. SCF calculations have been carried out with STO-3G and 4-31G basis sets, and Koopmans' theorem was applied to obtain the core-level binding energies. To evaluate the performance of the procedure SCF calculations were carried out on polyacrylic acid. The existence of oxygen-induced secondary substituent effects in the XPS-(ESCA-)spectra is discussed. A comparison with semi-empirical CNDO/2 results from Clark and Thomas has been made.     

Electronic structure of linear halogen compounds

Self consistent field molecular orbital calculations have been carried out for the ground electronic states for diatomic molecules XY, with X, Y=H, F, Cl, Br or I. Basis sets are critically discussed, and computed properties compared with experiment. The correlation between experimental ionization energies and those estimated through the use of Koopmans' theorem is given.     

Sur un traitement unifie des deplacements chimiques en spectrometrie photoelectronique de rayons—X (ESCA), des moments dipolaires et des polarisabilites

The simplest and most general model for interpreting ESCA chemical shifts, the physical meaning of which is very clear, also allows the discussion of dipole moments and polarisabilities. Sixty-eight ESCA chemical shifts of C_1s, N_1s, O_1s and F_1s in 41 differently-substituted compounds (?F, ?Cl, ?Br, ?OH, ?NH₂), saturated or unsaturated (aldehydes, ketones, acids), have been calculated with this model from electric charge distribution; the mean quadratic deviations are respectively ±1.1 eV for C, ±1.6 eV for N, ±0.8 eV for 0, ±0.7 eV for F.With this model, electric charge repartitions can be deduced from ESCA data, even for aromatic molecules. The calculated electric dipole moments for 12 fluorinated aromatic molecules agree very well with experimental results. Other data have been calculated for molecules for which experimental data are not yet available, including examples where heavy atoms are present.     

Core-valence correlation effects for molecules containing first-row atoms. Accurate results using effective core polarization potentials

The accuracy of employing effective core polarization potentials (CPPs) to account for the effects of core-valence correlation on the spectroscopic constants and dissociation energies of the molecules B₂, C₂, N₂, O₂, F₂, CO, CN, CH, HF, and C₂H₂ has been investigated by comparison to accurate all-electron benchmark calculations. The results obtained from the calculations employing CPPs were surprisingly accurate in every case studied, reducing the errors in the calculated valence D _e values from a maximum of nearly 2.5 kcal/mol to just 0.3 kcal/mol. The effects of enlarging the basis set and using higher-order valence electron correlation treatments were found to have only a small influence on the core-valence correlation effect predicted by the CPPs. Thus, to accurately recover the effects of intershell correlation, effective core polarization potentials such as the ones used in the present work provide an attractive alternative to carrying out computationally demanding calculations where the core electrons are explicitly included in the correlation treatment. Received: 11 May 1998 / Accepted: 27 July 1998 / Published online: 28 October 1998     

An extended-valence MC SCF procedure: determination of the dissociation energies of C2, N2, O2, and F2

A series of MC SCF calculations have been carried out on C₂, N₂, O₂, and F₂ with the goal of obtaining compact wavefunctions which recover a significant fraction of the electron correlation effects important for bond dissociation. The active orbital space is varied in size, with the largest spaces including the molecular orbitals derived from 2s, 2p, 3s, 3p and 4p atomic orbitals. Several basis sets ranging in size from 5s3p to 5s4p2d1f are investigated to determine the flexibility in the basis set needed with various choices of the active orbital space. The best extended-valence MC SCF (EVMC) dissociation energies are 0.2–0.5 eV less than the experimental values, indicating that further enlargement of the active orbital space is necessary to achieve 0.1 eV accuracy in the computed dissociation energies. The EVMC calculations reveal that, for the calculation of the dissociation energies, inclusion of non-valence orbitals is much more important for O₂ and F₂ than for C₂ and N₂. The EVMC results are compared with the predictions of full fourth-order perturbation theory, coupled cluster theory, and with the best available CI calculations.     

Cocrystals of 2,3,5,6‐tetrafluorobenzene‐1,4‐diol with diaza aromatic compounds

2,3,5,6‐Tetrafluorobenzene‐1,4‐diol easily forms cocrystals with heteroaromatic bases containing the pyrazine unit. In the 1:1 complexes with pyrazine, C₆H₂F₄O₂·C₄H₄N₂, (I), and quinoxaline, C₆H₂F₄O₂·C₈H₆N₂, (II), the crystal components are linked via O—H...N hydrogen bonds into one‐dimensional chains. With the largest base, phenazine, the 1:2 benzenediol–phenazine complex, C₆H₂F₄O₂·2C₁₂H₈N₂, (III), was obtained, with the molecules linked via O—H...N interactions into a discrete heterotrimer. In all three cocrystals, the two types of molecules are organized into layers via softer C—H...O and C—H...F interactions and π–π stacking interactions, with stronger hydrogen bonds linking molecules of adjacent layers. In (II) and (III), molecules are arranged into heterostacks, whereas in (I) separate stacks are formed by the heterocyclic base and the benzenediol molecule.     

Molecular Complexes of Fullerenes C60 and C70 with Saturated Amines

New molecular complexes of fullerenes C₆₀ and C₇₀ with leuco crystal violet (LCV, 1-3); leucomalachite green (LMG, 4-6); crystal violet lactone (CVL, 7); N,N,N′,N′-tetrabenzyl-p-phenylenediamine (TBPDA, 8, and 9); N,N,N′,N′-tetramethyl-p-phenylenediamine (TMPDA, 10, and 11); triphenylamine (TPA, 12, and 13); and substituted phenotellurazines (EPTA and TMPTA, 14, and 15) have been synthesized. Crystal structures have been solved for C₆₀ complexes with LMG (5, 6) TBPDA (8), TMPDA (10), and TPA (12). The C₆₀ molecules form closely packed double layers in 5 and 6, hexagonal layers in 10 and quasi-three-dimensional layers in 8 and 12. The substitution of disordered solvent molecules in the complexes with LMG (4, 5) by naphthalene ones results in the ordering of the C₆₀ molecules. According to IR-, UV-visible-NIR and ESR-spectroscopy the complexes have a neutral ground state. The spectra of 1-8, and 10 show intense charge transfer bands in the visible and NIR-range. On photoexcitation by white light (light-induced ESR (LESR) spectroscopy), 1 and 10 were shown to have an excited ionic state. The LESR signals were generated at light energies <2.25 eV indicating that the excited states in the complexes are realized mainly by direct charge transfer from donor to the C₆₀ molecule.     

Three new phosphoric triamides with a [C(O)NH]P(O)[N(C)(C)]2 skeleton: a database analysis of C—N—C and P—N—C bond angles

In N,N,N′,N′‐tetraethyl‐N′′‐(4‐fluorobenzoyl)phosphoric triamide, C₁₅H₂₅FN₃O₂P, (I), and N‐(2,6‐difluorobenzoyl)‐N′,N′′‐bis(4‐methylpiperidin‐1‐yl)phosphoric triamide, C₁₉H₂₈F₂N₃O₂P, (II), the C—N—C angle at each tertiary N atom is significantly smaller than the two P—N—C angles. For the other new structure, N,N′‐dicyclohexyl‐N′′‐(2‐fluorobenzoyl)‐N,N′‐dimethylphosphoric triamide, C₂₁H₃₃FN₃O₂P, (III), one C—N—C angle [117.08 (12)°] has a greater value than the related P—N—C angle [115.59 (9)°] at the same N atom. Furthermore, for most of the analogous structures with a [C(=O)NH]P(=O)[N(C)(C)]₂ skeleton deposited in the Cambridge Structural Database [CSD; Allen (2002). Acta Cryst. B 58 , 380–388], the C—N—C angle is significantly smaller than the two P—N—C angles; exceptions were found for four structures with the N‐methylcyclohexylamide substituent, similar to (III), one structure with the seven‐membered cyclic amide azepan‐1‐yl substituent and one structure with an N‐methylbenzylamide substituent. The asymmetric units of (I), (II) and (III) contain one molecule, and in the crystal structures, adjacent molecules are linked via pairs of N—H...O=P hydrogen bonds to form dimers.     

Vibrational relaxation dynamics of the X̃1∑g+ state of C3

The vibrational relaxation dynamics of the ground ¹∑_g⁺ electronic state of C₃ has been studied following IR multiple photon dissociation of allene. Wavelength and time resolved spectra, using dye laser-induced fluorescence are used to characterize the vibratioanl levels and their corresponding rise and decay rates. Vibrational relaxation rates are reported for C₃ (¹∑⁺_g, 100 or 110) in the presence of Ar, He, N₂, O₂ and C₂H₂, in addition to the reaction rate constant of C₃ (¹∑⁺_g. 000) with C₂H₂ of (2.2 ± 0.20) × 10_-14 cm³ molecule^?1 s^?1.     

Koopmans' defects in metal group VIII carbonyls—a many-body approach

The ionization potentials of iron pentacarbonyl ( 1 ), ethylene–iron tetracarbonyl ( 2 ), cobalt tetracarbonylhydride ( 3 ), and nickel tetracarbonyl ( 4 ) have been calculated using a Green's function perturbation method based on the INDO approximation. It is shown that the deviations from Koopmans' theorem are largest in the Co complex, while the smallest reorganization energies of strongly localized MO s with predominant metal 3d character are found in the Fe carbonyls 1 and 2 . The calculated Koopmans' defects are analyzed by an investigation of the relaxation terms of the self-energy part and are compared with previous INDO results for Cr, Mn, and Fe tricarbonyl derivatives. Additionally, orbital energies, bond indices, and net charges for the ground states of 1 – 4 are calculated and compared with experimental data.     

Twist‐chair conformation of the tetraoxepane ring remains unchanged in tetraoxaspirododecane diamines

A detailed structural analysis has been performed for N,N′‐bis(4‐chlorophenyl)‐7,8,11,12‐tetraoxaspiro[5.6]dodecane‐9,10‐diamine, C₂₀H₂₂Cl₂N₂O₄, (I), N,N′‐bis(2‐fluorophenyl)‐7,8,11,12‐tetraoxaspiro[5.6]dodecane‐9,10‐diamine, C₂₀H₂₂F₂N₂O₄, (II), and N,N′‐bis(4‐fluorophenyl)‐7,8,11,12‐tetraoxaspiro[5.6]dodecane‐9,10‐diamine, C₂₀H₂₂F₂N₂O₄, (III). The seven‐membered ring with two peroxide groups adopts a twist‐chair conformation in all three compounds. The lengths of the C—N and O—O bonds are slightly shorter than the average statistical values found in the literature for azepanes and 1,2,4,5‐tetraoxepanes. The geometry analysis of compounds (I)–(III), the topological analysis of the electron density at the (3, ?1) bond critical points within Bader's quantum theory of `Atoms in molecules' (QTAIM) and NBO (natural bond orbital) analysis at the B3LYP/6‐31G(d,2p) level of theory showed that there are n_O→σ*(C—O), n_N→σ*(C—O) and n_O→σ*(C—N) stereoelectronic effects. The molecules of compounds (I) and (III) are packed in the crystals as zigzag chains due to strong N—H…O and C—H…O hydrogen‐bond interactions, whereas the molecules of compound (II) form chains in the crystals bound by N—H…O, C—H…π and C—H…O contacts. All these data show that halogen atoms and their positions have a minimal effect on the geometric parameters, stereoelectronic effects and crystal packing of compounds (I)–(III), so that the twist‐chair conformation of the tetraoxepane ring remains unchanged.