Calculation of Vertical Ionization Potentials of Oxygen Difluoride,Difluoramine, and Difluoromethane by Local Density Approximation

The vertical ionization potentials of OF₂, HNF₂, and CH₂F₂ were computed by the deMon density functional program. The results are compared with earlier calculations and with experiment. The average absolute deviation of the 21 computed ionization potentials of the outer valence electrons from experiment is 0.44 eV, which compares well with 0.37 eV for frozen-orbital configuration-interaction calculations. Although this performance is not as good as perturbation corrections to Koopmans' theorem, the computation requirements are much less demanding.     

Extended Koopmans' theorem ionization potentials for beryllium atom shake-up transitions

The ionization potentials were calculated for Be using the extended Koopmans' theorem (EKT ) using several full configuration interaction (CI ) and multiconfigurational-self-consistent-field (MCSCF ) wave functions as reference wave functions. The wave functions used account for 89.7–96.7% of the correlation energy. Comparisons are made with experimental values and with δCI values calculated as the difference in energy obtained from CI wave functions for Be and Be⁺. The best EKT IP differed from the δCI value by 0.0003 eV for the lowest IP and by 0.0006 eV for ionization into the lowest ²P state of Be⁺. A calculation of ionization into the second ²P state of Be⁺ requires diffuse orbitals that are unimportant in the wave function for the ground state of Be. This results in small natural orbital occupation numbers for natural orbitals needed in the EKT calculation. © 1994 John Wiley & Sons, Inc.     

The multiconfigurational spin tensor electron propagator method (MCSTEP): Comparison with extended Koopmans' theorem results

Summary We applied the multiconfigurational spin tensor electron propagator method (MCSTEP) for determining the lowest few (in energy) vertical ionization potentials (IPs) of HF, H₂O, NH₃, CH₄, N₂, CO, HNC, HCN, C₂H₂, H₂CO, and B₂H₆. We chose these molecules so that we could compare MCSTEP IPs with recently reported extended Koopmans' theorem (EKT) IPs on the same molecules. Using standard Dunning core-valence basis sets with relatively small complete active spaces, MCSTEP results are in very good to excellent agreement with experiment. These MCSTEP IPs are obtained using matrices no larger than 400 × 400. EKT matrices are even smaller; however, to obtain similar but generally slightly worse agreement with experiment, fairly large active spaces are required with EKT.     

Minimal basis study of inner-shell ionization potentials for molecules containing sulfur: S,S-Diphenyl-N-p-Tolylsulfonyl-Sulfilimine

Ab initio calculations with a minimal (STO -3G) basis set on a number of sulfur-containing molecules are used to show that Koopmans' theorem and minimal basis calculations may be a simple but adequate way of obtaining inner-shell ionization potentials and chemical shifts of large molecules. The x-ray photoelectron spectrum of (C₆H₅)₂SNSO₂C₆H₄CH₃ is discussed with reference to an ab initio SCF minimal basis calculation on the model molecule H₂SNSO₂H.     

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.     

Natural energy orbitals and the one-particle Green's function

It is shown how the properties of the one-particle Green's function lead naturally to the definition of the so-called natural energy orbitals. These orbitals allow the fully correlated total energy of a system to be written in Hartree–Fock-like fashion and might therefore provide a bridge between sophisticated correlated wave functions and approximate theories of chemical structure and reactivity based on a Hartree–Fock-like energy expression. Moreover these orbitals form the basis for a self-consistent scheme to calculate the one-particle Green's function. The relation between these natural energy orbitals and the extended Koopmans' theorem is considered. Finally it is shown that the exactness of the lowest extended Koopmans' ionization potential implies the linear independence of the corresponding Dyson orbital from all other Dyson orbitals.     

Average dipole polarizabilities from the unsold approximation and ab initio data

An approximate static dipole polarizability equation is developed on the basis of the Unsold approximation, and is cast in closed shell LCAO MO SCF formalism. A brief study is made of the use of Koopmans' theorem as a means of obtaining an average ionization energy, necessary in the polarizability equation presented. Average polarizabilities for the systems He, Ne, H₂, HF, H₂O, NH₂, CH₄, HCN, N₂, C₂H₂, C₂H₄, C₂H₆, C₆H₆, and C₆H₅F are calculated from the dipole polarizability expression developed using a small 4-31G basis set level. Results show good agreement with experimental data.     

Ground states of molecules. 53.MNDO calculations for molecules containing chlorine

MNDO calculations of heats of formation, dipole moments, ionization potentials, and structures are reported for a wide range of compounds containing chlorine in its characteristic valence state (Cl^I) and one or more of the elements H, B, Be, C, N, O, and F. The calculated errors in the heats of formation and the dipole moments are not significantly greater than those previously reported for compounds containing no chlorine. First vertical ionization potentials were on average 0.95 eV too high. The ordering of higher cationic states was found to be correct, even for species such as Cl₂O, Cl₂, and HOCl, where ab initio–Koopmans' theorem calculations predict the incorrect ordering. The calculated energies and geometries of compounds such as CIF₃ are qualitatively incorrect, probably because of the lack of 3d atomic orbitals in the orbital basis set.     

The extended Koopmans' theorem Fock operator

By expanding the wave function of a system of N particles in terms of products of functions of one and (N-1) particles, the one-particle, nonlocal operator F?_EKT (extended Koopmans' theorem) is determined. It is shown that although this operator is nonhermitian, its eigenvalues and eigenfunctions represent the ionization energies and occupied orbitals, respectively. The eigenfunctions of F?_EKT are the one-particle functions that enter into the expansion of the wave function of the system as partners of the (N-1)-particle wave functions. The eingenvalues are also one-particle energies that, multipled by the orbital occupancy probalities, enter the expression for the total N-particle energy of the system.     

Assessment of the extended Koopmans' theorem for the chemical reactivity: Accurate computations of chemical potentials,chemical hardnesses,and electrophilicity indices

The extended Koopmans' theorem (EKT) provides a straightforward way to compute ionization potentials and electron affinities from any level of theory. Although it is widely applied to ionization potentials, the EKT approach has not been applied to evaluation of the chemical reactivity. We present the first benchmarking study to investigate the performance of the EKT methods for predictions of chemical potentials (μ) (hence electronegativities), chemical hardnesses (η), and electrophilicity indices (ω). We assess the performance of the EKT approaches for post‐Hartree–Fock methods, such as Møller–Plesset perturbation theory, the coupled‐electron pair theory, and their orbital‐optimized counterparts for the evaluation of the chemical reactivity. Especially, results of the orbital‐optimized coupled‐electron pair theory method (with the aug‐cc‐pVQZ basis set) for predictions of the chemical reactivity are very promising; the corresponding mean absolute errors are 0.16, 0.28, and 0.09 eV for μ, η, and ω, respectively. © 2015 Wiley Periodicals, Inc.     

Perturbation corrections to koopmans theorem. V. A study with large basis sets

The vertical ionization potentials of N₂, F₂ and H₂O were calculated by perturbation corrections to Koopmans' theorem using six different basis sets. The largest set used includes several sets of polarization functions. Comparison is made with measured values and with results of computations using Green's functions.     

Koopmans' theorem ionization potentials of methyl and silyl halides,chalcogenides, amines,and phosphines: An ab InitioSCF study

Koopmans' theorem ionization potentials have been calculated for a series of hydrides, methyls, and silyls H_nX, (CH₃)_nX, and (SiH₃)_nX (X = F, Cl, n = 1; X = O, S, n = 2; X = N, P, n = 3), together with some mixed species (MH₃)_nXH_3-n (X = N, P; M = C, Si) using ab initio SCF methods. The calculated values give excellent agreement with experimental values without the inclusion of d functions. For the chlorides, HCl, CH₃Cl, and SiH₃Cl, the values vary rather little over a wide range of basis sets, and are unaffected by the inclusion of d functions.     

Theoretical calculation of vertical ionization potentials of B2H6 by means of ΔESCF procedures

The vertical ionization potentials (IPS ) of B₂H₆ are calculated by means of the ΔE_SCF procedure, within the scheme of ab initio LCAO-MO-HF-SCF . The basis set used is LEMAO -3G. The scaling factors of the various atomic orbitals for the ground state and for the various hole states are optimized independently. The iteration procedure is specially designed to avoid the changes of the symmetry of the remaining occupied orbitals. The 1 ag (B1s) hole is found to be localized. The vertical IP of the 1 ag electron is calculated to be 196.5 eV, in fair agreement with experimental value. The D_2h symmetry is thereby broken and reduced to C_2V symmetry. The valence holes are found to be delocalized. The calculated vertical IPS are: 21.781, 16.974, 14.842, 14.389, 13.599, and 12.380 eV for the 2ag, 2b1u, 1b3u, 1b2u, 3ag, and 1b3g electrons, respectively. The agreement with experimental values is much better than the Koopmans' values. All these results are in favor of the concept that the nature of the convelent bond should be considered as a result of the mutual interactions and mutual conditioning between the wave nature of the electronic motion on the one side and the various attractive and repulsive factors on the other side.     

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.     

The extended Koopmans' theorem Fock operator and the generalized overlap amplitude one-electron operator

The wave function of a system may be expanded in terms of eigenfunctions of the N −1 electron Hamiltonian times one-particle functions known as generalized overlap amplitudes (GOAS). The one-electron operator whose eigenfunctions are the GOAS is presented, without using an energy-dependent term as in the one-particle Green function or propagator approach. It is shown that this operator and the extended Koopmans' theorem (EKT) one-electron operator are of similar form, but perform complementary roles. The GOA operator begins with one-electron densities and total energies of N −1 electron states to generate the two-matrix and total energy of an N-electron state. The EKT operator begins with the two-matrix of an N-electron state to generate one-electron densities and ionization potentials (or approximations thereto) for N −1 electron states. However, whereas the EKT orbitals must be linearly independent, no such restriction applies to the GOAS. © 1996 John Wiley & Sons, Inc.     

Approximate Self-Consistent Molecular Orbital Theory II. CNDO-MO Calculation of Methane Chlorine Derivatives

The CNDO-MO method with s-p separation model modification described in our former work¹⁾ is used here. Methane and it's chlorine derivatives are selected as the model molecules for such calculation. The nuclear coordinates are chosen from microwave spectroscopic data²⁾. Both the self consistent behavior and the invariance of orthogonal transformation²⁾ are quite successfully by preformed through the computation procedure. The ionization potentials predicted by Koopmans' theorem are reasonably good. The charge distribution and dipole moments of each case are calculated, and the results obtained by variation of bond parameter β are compared with the available experimental data satisfactorily.