Electron propagator calculations show that alkyl substituents alter porphyrin ionization energies

The effect of alkyl substituents on the four lowest vertical ionization energies of porphyrins is determined with ab initio electron propagator calculations on porphine and octamethylporphyrin. With the use of the partial third-order approximation, predicted ionization energies are in close agreement with recent photoelectron spectra. These data and the associated Dyson orbitals, which describe changes in electronic structure that accompany photoionization, enable assignment of photoelectron spectra and determination of alkyl-induced shifts. Hyperconjugation is most evident in the Dyson orbitals associated with the third and fourth ionization energies of octamethylporphyrin and is least prominent in the Dyson orbital of the second ionization energy. There is a positive correlation between the shift in an ionization energy produced by alkyl substitution and the degree of hyperconjugation in the associated Dyson orbital. Alkyl substitutions, therefore, may be employed to adjust the ionization energies of porphyrins and, consequently, their reactivity patterns that depend on charge-transfer capabilities and disposition to electrophilic attack.     

Determining partial differential cross sections for low-energy electron photodetachment involving conical intersections using the solution of a Lippmann-Schwinger equation constructed with standard electronic structure techniques

A method for obtaining partial differential cross sections for low energy electron photodetachment in which the electronic states of the residual molecule are strongly coupled by conical intersections is reported. The method is based on the iterative solution to a Lippmann-Schwinger equation, using a zeroth order Hamiltonian consisting of the bound nonadiabatically coupled residual molecule and a free electron. The solution to the Lippmann-Schwinger equation involves only standard electronic structure techniques and a standard three-dimensional free particle Green's function quadrature for which fast techniques exist. The transition dipole moment for electron photodetachment, is a sum of matrix elements each involving one nonorthogonal orbital obtained from the solution to the Lippmann-Schwinger equation. An expression for the electron photodetachment transition dipole matrix element in terms of Dyson orbitals, which does not make the usual orthogonality assumptions, is derived.     

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.     

Electric dipole polarizability of the hydrogen molecule by many-body perturbation theory

Many-body perturbation theory is used to calculate the static electric dipole polarizability of the hydrogen molecule with a basis set of gaussian orbitals. Corrections complete through second order in electron correlation are calculated, and partial summation of certain classes of diagrams are extensively explored. The results are discussed in connection with the geometric approximation incorporating higher-order corrections.     

Application of the many-body perturbation theory by using localized orbitals

Diagrammatic formulation of the many-body perturbation theory is investigated when both the occupied orbitals and the virtual ones are localized, i.e., they are unitary transforms of the canonical Hartree–Fock orbitals. All diagrams representing ground state correlation energy can be generated through fifth order. For cyclic polyenes C₆H₆ and C₁₀H₁₀ as model systems, the energy corrections are calculated in the Pariser–Parr–Pople approximation for a wide range of the coupling constant β^?1, through fourth order including some fifth order terms. The results are compared to those obtained by other methods: perturbation theory by using canonical orbitals and full CI. The effect of neglecting contributions from orbitals localized into neighboring sites is also studied.     

Beyond Förster resonance energy transfer in linear nanoscale systems

The line dipole approximation is used to investigate analytical corrections to the F?rster energy transfer rate, k, derived via the point dipole approximation. It is shown that that for molecules whose conjugation length, L, is much larger than the separation, R, between molecules the line dipole approximation predicts k ~ (RL)?2 ~ (RN)?2 (where N is the number of conjugated monomer units). This is in contrast to the point dipole approximation, which predicts k ~ L2R?? ~ N2R??.     

Dyson orbitals for ionization from the ground and electronically excited states within equation-of-motion coupled-cluster formalism: theory, implementation, and examples

Implementation of Dyson orbitals for coupled-cluster and equation-of-motion coupled-cluster wave functions with single and double substitutions is described and demonstrated by examples. Both ionizations from the ground and electronically excited states are considered. Dyson orbitals are necessary for calculating electronic factors of angular distributions of photoelectrons, Compton profiles, electron momentum spectra, etc, and can be interpreted as states of the leaving electron. Formally, Dyson orbitals represent the overlap between an initial N-electron wave function and the N-1 electron wave function of the corresponding ionized system. For the ground state ionization, Dyson orbitals are often similar to the corresponding Hartree-Fock molecular orbitals (MOs); however, for ionization from electronically excited states Dyson orbitals include contributions from several MOs and their shapes are more complex. The theory is applied to calculating the Dyson orbitals for ionization of formaldehyde from the ground and electronically excited states. Partial-wave analysis is employed to compute the probabilities to find the ejected electron in different angular momentum states using the freestanding and Coulomb wave representations of the ionized electron. Rydberg states are shown to yield higher angular momentum electrons, as compared to valence states of the same symmetry. Likewise, faster photoelectrons are most likely to have higher angular momentum.     

Gauge invariant gaussian orbitals and the ab initio calculation of diamagnetic susceptibility for molecules

It is shown that gauge terms can be introduced into the Gaussian functions used as the basis functions for an ab initio calculation of the energy of a molecule in the presence of a uniform magnetic field so that all the integrals become independent of the origin of the vector potential. The perturbation treatment of the diamagnetic susceptibility is considered in the molecular orbital approximation. The results show that the susceptibility can be calculated using only the unperturbed orbitals and their first-order corrections. All the integrals that arise can be expressed in terms of known functions.     

Frozen core and effective core potentials in symmetry-adapted perturbation theory

The application of the frozen-core approximation (FCA) and effective core potentials (ECPs) within symmetry-adapted perturbation theory (SAPT) has been investigated and implemented. Unlike in the case of conventional electronic-structure theories, the development of a frozen-core version of SAPT is not straightforward. In particular, the FCA realizations neglecting excitations from core orbitals and restricting all summation indices to valence orbitals only are no longer equivalent. It is shown that it is necessary in SAPT to keep some terms containing products of the valence orbitals of one monomer and the core orbitals of the other one in the exchange-energy components. When these terms are included or, equivalently, the "infinite-excitation-energy" approximation omitting only the excitations from the core orbitals is used, the accuracy of the frozen-core approximation in SAPT matches that obtained in supermolecular perturbational and coupled-cluster methods. If these terms are neglected, i.e., within the "index-range-restriction" approximation, several exchange corrections are significantly underestimated. When ECPs are used in SAPT, the accuracy of the interaction energies is as good as in conventional supermolecular methods, provided that the residual supermolecular Hartree-Fock term is included. We have found that only some types of ECPs can be reliably used for calculations of interaction energies both in SAPT and in supermolecular approaches. For systems containing heavy atoms, both FCA and the use of ECPs lead to very significant savings of computer time.     

Relativistic correlation effects on the hyperfine structure and electric dipole transitions in Cs and Tl

A discrete numerical basis set is a versatile tool for many-body calculations. Here it is used to calculate second-order energy corrections and to construct approximate Brueckner orbitals for Cs and Tl in a relativistic framework. These orbitals, which often account for a large part of the correlation effects, are then used to evaluate the hyperfine structure and electric dipole transition matrix elements for a few low-lying states. The correlation effects were combined with the RPA diagrams, which account for the response of the orbitals to the external perturbation, and the results are compared with other calculations and with experiment. For Cs, the results are in good agreement with earlier work, whereas for the more complicated system Tl we find significantly larger contributions from the modification of the valence orbitals to approximate Brueckner orbitals.     

Second-order shakeup terms in electron propagator calculations on F2 and H2O2

A new approximation of the electron propagator includes second-order terms in the superoperator Hamiltonian matrix that are not present in the nondiagonal, renormalized method (NR2) of J. Chem. Phys. 108 , 1008 (1998). These terms are not difficult to calculate and resemble expressions obtained with various propagator and coupled-cluster formalisms. Their inclusion produces larger, more accurate vertical ionization energies of F₂ and H₂O₂. Cancellations between the second-order terms considered here and the first-order terms present in the NR2 method reduce the importance of shakeup operators in describing the first few cationic states of these molecules. Dyson orbitals for ²A final states of H₂O₂ exhibit qualitatively important mixings between canonical orbitals. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 175–182, 1998     

Core-shell photoabsorption and photoelectron spectra of gas-phase pentacene: experiment and theory

The C K-edge photoabsorption and 1s core-level photoemission of pentacene (C22H14) free molecules are experimentally measured, and calculated by self-consistent-field and static-exchange approximation ab initio methods. Six nonequivalent C atoms present in the molecule contribute to the C 1s photoemission spectrum. The complex near-edge structures of the carbon K-edge absorption spectrum present two main groups of discrete transitions between 283 and 288 eV photon energy, due to absorption to pi* virtual orbitals, and broader structures at higher energy, involving sigma* virtual orbitals. The sharp absorption structures to the pi* empty orbitals lay well below the thresholds for the C 1s ionizations, caused by strong excitonic and localization effects. We can definitely explain the C K-edge absorption spectrum as due to both final (virtual) and initial (core) orbital effects, mainly involving excitations to the two lowest-unoccupied molecular orbitals of pi* symmetry, from the six chemically shifted C 1s core orbitals.     

On the direct calculation of localized HF orbitals in molecule clusters,layers and solids

It is shown that the computational effort involved in HF calculations can be considerably reduced by applying the following concepts: 1) the use of a localization operator for the direct determination of localized non-orthogonal HF orbitals, 2) the approximation of the interaction potential between different localization centres by a Hartree-like ansatz, 3) the successive calculation of many-body corrections to molecular properties such as the total energy. A numerical application to LiH layers and solid LiH is described.     

Design of an exchange functional with correct asymptotics

Knowledge of asymptotic conditions on exchange allows for a better design of exchange energy expressions in density functional theory. By working inside an exchange-only framework, the fulfillment of such conditions by some of the most widely used exchange functionals is discussed. In turn, we propose a model expression which partially meets the energetics and asymptotics of both the exchange energy density and potential. Improvement upon the local spin density approximation without the use of generalized gradient corrections is also presented. Hartree-Fock orbitals are employed to build electron densities. © 1997 John Wiley & Sons, Inc.     

On the relativistic corrections to the cross-section for inelastic scattering of photons on atomic electrons

The relativistic cross-section for inelastic photon scattering on bound electrons is reconsidered, and lowest-order corrections to the sudden-impulse approximation are derived. These corrections stem from including the presence of the external (Coulombic) field in the electron propagator that propagates the intermediate states of the scattering process. We find that these corrections are of the order Zα with respect to the result obtained within the impulse approximation, and are an order of magnitude larger than the corrections obtained previously by inclusion of the binding effects in the initial state only.     

Multiple basis sets in calculations of triples corrections in coupled-cluster theory

Multiple basis sets are used in calculations of perturbational corrections for triples replacements in the framework of single-reference coupled-cluster theory. We investigate a computational procedure, where the triples correction is calculated from a reduced space of virtual orbitals, while the full space is employed for the coupled-cluster singles-and-doubles model. The reduced space is either constructed from a prescribed unitary transformation of the virtual orbitals (for example into natural orbitals) with subsequent truncation, or from a reduced set of atomic basis functions. After the selection of a reduced space of virtual orbitals, the singles and doubles amplitudes obtained from a calculation in the full space are projected onto the reduced space, the remaining set of virtual orbitals is brought into canonical form by diagonalizing the representation of the Fock operator in the reduced space, and the triples corrections are evaluated as usual. The case studies include the determination of the spectroscopic constants of N₂, F₂, and CO, the geometry of O₃, the electric dipole moment of CO, the static dipole polarizability of F⁻, and the Ne⋯Ne interatomic potential. Received: 28 December 1996 / Accepted: 8 April 1997     

Large-scale RPA calculations of chiroptical properties of organic molecules: Program RPAC

The computational considerations involved in calculating ordinary and rotatory intensities and electronic excitation energies in the random phase approximation (RPA ) are examined. We employ a localized orbital formulation in order to analyze the results in terms of local and charge-transfer excitations. Occupied orbitals are localized by the Foster–Boys procedure. The virtual space is transformed into a localized “valence” set that maximizes dipole strengths with the occupied counterparts, and a delocalized remainder. The two-electron integral transformation is performed with an efficient algorithm, based on Diercksen's, that generates only the particle–hole-type integrals required in the RPA . The lowest solutions of the RPA equations are obtained iteratively using a modification of the Davidson-Liu simultaneous vector expansion method. This allows the inclusion of the entire set of particle–hole states supported by a basis set of up to 102 orbitals. Calculations at this level give better excitation energies and intensities than SDCI methods, at substantial savings in computational effort. Comparative timings, computed results and analysis in terms of localized orbitals are given for planar and distorted ethylene using extended atomic orbital bases including diffuse functions. The results for planar ethylene are in excellent agreement with experiment.     

Degenerate states perturbation theory and continued fractions

An extension is made for degenerate levels of a recently proposed method for calculating higher-order terms of eigenvalues in a perturbation system with discrete energy levels. The method is used for calculating ground-state energy eigenvalue corrections for a rigid rotator which has a dipole ajid interacts with an applied electric field.     

Orbital signatures of methyl in L-alanine

Molecular orbital signatures of the methyl substituent in L-alanine have been identified with respect to those of glycine from information obtained in coordinate and momentum space, using dual space analysis. Electronic structural information in coordinate space is obtained using ab initio (MP2/TZVP) and density functional theory (B3LYP/TZVP) methods, from which the Dyson orbitals are simulated based on the plane wave impulse approximation into momentum space. In comparison to glycine, relaxation in geometry and valence orbitals in L-alanine is found as a result of the attachment of the methyl group. Five orbitals rather than four orbitals are identified as methyl signatures. That is, orbital 6a in the core shell, orbitals 11a and 12a in the inner valence shell, and orbitals 19a and 20a in the outer valence shell. In the inner valence shell, the attachment of methyl to glycine causes a splitting of its orbital 10a' into orbitals 11a and 12a of L-alanine, whereas in the outer valence shell the methyl group results in an insertion of an additional orbital pair of 19a and 20a. The frontier molecular orbitals, 24a and 23a, are found without any significant role in the methylation of glycine.     

Limitations on the validity of the non-relativistic dipole approximation for photoelectron angular distributions

We present results which exhibit hazards in the use of the non-relativistic dipole approximation in the interpretation of experimental photoelectron angular distributions. Significant deviations from the non-relativistic dipole approximation occur for both low and high Z atoms. In light elements these effects are found in the keV range and even below. In heavy elements they are found even for energies very close to threshold. For total cross sections, in contrast to this angular distribution situation, the surviving integrated relativistic and multipole corrections tend to cancel, so that the non-relativistic dipole approximation holds to surprisingly high energies.