Atomic parameters for semi-empirical SCF-LCAO-MO calculations

Atomic core and electron-repulsion components of the Hamiltonian matrix elements, for s and p valence orbitals, have been evaluated from atomic valence-state energies. Atomic parameters for semi-empirical, self-consistent field, molecular-orbital calculations with the complete neglect of differential overlap (CNDO) approximation are given for non-transition elements of the first four rows of the periodic table. The application of these parameters to the evaluation of interatomic parameters for calculations with the CNDO approximation is discussed.

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Zusammenfassung Für die Elemente der ersten vier Reihen des Periodensystems (mit Ausnahme der Übergangselemente) werden atomare Parameter für halbempirische SCF-MO Rechnungen mit der CNDO Näherung gegeben. Es wird die Anwendung dieser Parameter zur Bestimmung interatomarer Größen, die für Rechnungen mit der CNDO Näherung gebraucht werden, diskutiert.

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Résumé Les énergies des états de valence atomiques sont utilisées pour évaluer les éléments de la matrice hamiltonienne dans la base des orbitales de valence s et p. Des paramètres atomiques sont fournis pour les éléments des quatre premières périodes de la table périodique (á l'exception des éléments de transition). Ces paramètres sont utilisables pour des calculs semi-empiriques dans la méthode SCF-MO avec «recouvrement différentiel nul» (CNDO). L'application de ces paramètres à l'évaluation de paramètres interatomiques pour des calculs dans l'approximation CNDO est discutée.

     

SCF calculations of aromatic hydrocarbons the variable β approximation

The transition energies and intensities of naphthalene, anthracene, phenanthrene, pyrene, and azulene are calculated with a variable modification of the Pariser-Parr-Pople method. In this procedure each is determined from the bond order after every iteration. The dependence of on bond order is given by = –0.51 p + A ₀ eV where A ₀ is –1.90 eV (naphthalene and azulene), –1.84 eV (anthracene and phenanthrene), and –1.82 eV (pyrene). Precise knowledge of the molecular geometry is not required and the results are in good agreement with experiment.

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Zusammenfassung Die elektronischen Anregungsenergien sowie die zugehörigen Intensitäten von Naphthalin, Anthrazen, Phenantren, Pyren und Azulen wurden mit der Modifikation der variablen der Pariser-Parr-Pople Methode berechnet, bei welcher die -Werte nach jedem Iterationsschritt als Funktion der Bindungsordnung neu berechnet werden. Ihre Abhängigkeit ist durch = –0,51 p + A ₀ eV gegeben, wobei A ₀ –1,90 (Naphthalin und Azulen), –1,84 (Anthrazen und Phenantren) bzw. –1,82 (Pyren) ist. Für das Verfahren ist die genaue Kenntnis der Geometrie des Moleküls nicht vonnöten und die Resultate befinden sich in guter Übereinstimmung mit dem Experiment.

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Résumé Nous avons calculé les énergies et intensités des transitions électroniques de naphthalène, Anthracène, phénanthrène, pyrène et azulène par une méthode PPP modifiée, où les sont déterminés des indices de liaison p après chaque itération: = –0,51 p + A ₀ eV, où A ₀ = –1,90 (pour naphthalène et azulène), –1,84 (anthracène et phénanthrène) et –1,82 (pyrène), respectivement. On n'a pas besoin des géometries exactes des molécules. Les résultats s'accordent bien à l'expérience.

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Supported by the U.S. Atomic Energy Commission and National Science Foundation.     

Direct algorithm for the random-phase approximation

An algorithm for calculating excitation energies and transition moments in the random-phase approximation (RPA) of the polarization propagator is presented. The algorithm includes direct solution of the RPA eigenvalue problem and direct evaluation of products of superoperator Hamiltonian matrices with excitation vectors. Given sufficient memory, only one integral evaluation step per iteration is needed. Illustrative calculations on the excitation energies and oscillator strengths of ethylene are presented. © 1996 John Wiley & Sons, Inc.     

Molecular mechanics (MM3) calculations on conjugated hydrocarbons

The MM3 molecular mechanics program has been extended to conjugated systems. A VESCF method is applied to the pi-system to calculate bond orders, from which various stretching and torsional parameters are obtained. The procedure gives somewhat better results than the analogous MM2 calculations. It has been applied to a study of 81 compounds of aromatic and other conjugated hydrocarbons, as well as 45 alkenes and unconjugated polyenes. The structures calculated are generally in good agreement with experiment, and the heats of formation of these compounds can be calculated with a rms value of 0.62 kcal/mol, which may be compared with the average experimental error of 0.61 kcal/mol. In addition, vibrational frequencies for five representative conjugated model structures are calculated, with an rms value of 46 cm^?1, and from these, other properties such as entropy can be calculated.     

Theoretical calculations of magnetic moments of mono-cyclic conjugated hydrocarbons

The magnetic moments of excited states of mono-cyclic non-alternant conjugated hydrocarbons with 3-9 carbon atoms were theoretically calculated using wavefunctions determined on the basis of the LCAO MO method. The predicted value is in good agreement with experiment for the tropylium cation.     

Differential photoionization cross section calculations for HI using the random-phase approximation with L2 basis functions

The photoionization cross sections and asymmetry parameters of the three main valence ionization processes in HI, corresponding to the formation of, respectively, 6π, 11σ, and 10σ holes, were calculated in the random-phase approximation (RPA). Our particular computational procedure, based on solving the integral equation for the half on the shell K-matrix upon a grid of points supplied by an L² basis set calculation, affords recovery of the electronic continuum degeneracy of the final states. This makes it possible to compute the differential ionization cross section at any energy up to the fourth ionization threshold, allowing for the interaction of the three channels considered. The total cross section obtained by applying the Stieltjes imaging procedure to the discrete spectrum yielded by the RPA is also reported. © 1996 John Wiley & Sons, Inc.     

AB initio calculations of oscillator and rotatory strengths in the random-phase approximation: planar and twisted butadiene

Minimal basis set (STO-4G) ab initio calculations in the random-phase approximation (RPA) are presented for the ordinary and rotatory intensities of the low-lying electronic transitions of twisted cis-butadiene, and planar trans-butadiene. The formally equivalent intensities agree much better in the RPA than in either monoexcited CI or Hartree-Fock virtual orbital calculations. Comparisons with other work are given, and an explanation is suggested for the sensitivity of the rotatory strengths to substituents.     

On the importance of correlation effects for the parameters of semi-empirical molecular orbital calculations

The one- and two-center coulomb repulsion parameters of semi-empirical molecular orbital calculations are commonly assumed to incorporate some correlation effects. It is shown that the horizontal correlation energy in a two-electron diatomic molecule can indeed be combined with the one- and two-center coulomb integrals to yield correlated parameters. However, the theoretical expressions for these parameters show a dependence on the internuclear separation which is strongly at variance with the common assumptions. The results indicate that a theoretical elucidation of the semi-empirical parameters is not likely to be found by consideration of correlation effects in a single electronic state.

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Zusammenfassung I.a. wird angenommen, daß die Parameter semiempirischer MO-Rechnungen Korrelationseffekte miterfassen. Für H₂ wird gezeigt, daß die horizontale Korrelation sich tatsächlich durch Verwendung korrelierter Parameter beschreiben läßt. Jedoch unterscheidet sich die theoretische Abhängigkeit dieser Parameter vom Kernabstand von der üblicherweise angenommenen. Es ist nicht möglich, die Parameter semiempirischer MO-Methoden durch Untersuchung der Korrelation nur eines Zustandes theoretisch zu errechnen.

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Résumé Les paramètres coulombiens de répulsion à un et deux centres des calculs semi-empiriques d'orbitales moléculaires sont habituellement supposés tenir compte de certains effets de corrélation. On montre que l'énergie de corrélation horizontale dans une molécule diatomique à deux électrons peut cependant être combinée avec les intégrales de coulomb à un et deux centres pour fournir des paramètres corrélés. Mais les expressions théoriques pour ces paramètres montrent une variation avec la distance internucléaire très différente de celle supposée habituellement. Ces résultats montrent qu'un éclaircissement théorique des paramètres semiempiriques ne sera sans doute pas obtenu par la considération des effets de corrélation dans un état électronique unique.

     

Extended Hückel calculations of the ionization potentials of some conjugated hydrocarbons

The prediction of ionization potentials of conjugated hydrocarbons using extended Hückel theory is reevaluated. Consequently, two major modifications to the theory are proposed and then tested on five sample molecules. Allowance for distinct sigma and pi orbital parameters as well as for diagonal and off-diagonal parameters constitute the changes examined and are shown to arise naturally from the theory. Subsequent testing of the reproduction of photoelectron spectra indicates significant improvements over previous usage of extended Hückel theory.     

Uncoupled Hartree-Fock calculations of the ring current contribution to the chemical shifts in conjugated hydrocarbons

Uncoupled Hartree-Fock perturbation theory is adapted for the calculation of the ring current contribution to the chemical shifts in a number of conjugated hydrocarbons. The results compare favourably with those of the coupled form of the theory. It is also shown that the Hückel approach may be modified so as to give values close to those of the SCF theory.

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Zusammenfassung Für einige konjugierte Kohlenwasserstoffe wird zur Berechnung des Anteils des Ringstroms an der chemischen Verschiebung die ungekoppelte Hartree-Fock-Störungstheorie verwandt. Die Ergebnisse stimmen gut mit denen überein, die man mit der gekoppelten Form der Theorie erhält. Ferner wird gezeigt, daß der Ansatz nach Hückel derart modifiziert werden kann, daß die Ergebnisse den aus der SCF-Theorie erhaltenen nahekommen.

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Résumé La théorie de perturbation Hartree-Fock non couplé est adaptée pour le calcul de la contribution du «courant cyclique» aux déplacements chimiques dans un certain nombre d'hydrocarbures conjugués. Les résultats se comparent favorablement à ceux de la théorie de Hartree-Fock couplé. On montre que par ailleurs l'approximation de type Hückel peut être modifiée de manière à donner des valeurs proches de celles de la théorie SCF.

     

LCAO-MO-SCF-CI semi-empirical π-electron calculations on heteroaromatic systems

The electronic spectra and structure for phenol, the three dihydroxybenzene isomers, and - and -naphthol have been calculated using a modification of the Pariser-Parr-Pople method. Core integrals are defined to be essentially independent of geometry and orthogonalized atomic orbitals are used. The electronic transitions considered involve singlet-singlet and triplet-triplet ^* excitations. A limited configuration interaction has been included, involving either single electron excitations or both single and double electron excitations between the two highest occupied and the two lowest unoccupied molecular orbitals. Agreement between calculated and experimental values is good, and calculated values for oscillator strengths are considerably improved when double electron excitations are admitted.

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Zusammenfassung Die Elektronenspektren und Struktur von Phenol, den drei Isomeren des Dihydroxybenzols und - und -Naphthol wurden mit einer Modifikation der PPP-Methode berechnet. Die Rumpfintegrale werden so definiert, daß sie im wesentlichen unabhängig von der Geometrie sind; es werden orthogonalisierte Atomorbitale benutzt. Die betrachteten Elektronenübergänge enthalten Singulett-Singulett- und Triplett-Triplett- ^*-Übergänge. Es wurde eine begrenzte Konfigurationswechselwirkung eingeschlossen, die nur Einelektronen- oder Ein- und Zweielektronenanregung zwischen den beiden höchsten besetzten und den beiden niedrigsten unbesetzten MO's enthält. Es besteht gute Übereinstimmung von berechneten und experimentellen Daten. Die berechneten Werte für Oszillatorenstärken werden erheblich verbessert, wenn man Zweielektronenanregung einbezieht.

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Résumé Les spectres électroniques et les structures du phénol, des trois dihydroxybenzènes isomères, de l' et du naphtol ont été calculé pour une variante de la méthode de Pariser-Parr-Pople. Les intégrales de coeur sont définies de manière à être indépendantes de la géométrie et des orbitales atomiques orthogonalisées sont employées. On considère les transitions électroniques ^* singulet-singulet et triplet-triplet. Une interaction de configuration limitée a été effectuée en considérant soit des minoexcitations soit des mono et des diexcitations de la plus haute orbitale occupée aux deux orbitales libres les plus basses. L'accord entre les valeurs calculées et les valeurs expérimentales est bon, et les valeurs calculées des forces oscillatrices sont considérablement améliorées lorsque l'on tient compte des états diexcités.

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This investigation was supported by a National Science Foundation grant, No. GB-4065. Abstracted in part from the Ph. D. thesis of G. W. Pukanic, Duquesne University, 1967.     

LCAO-MO-SCF-CI semi-empirical π-electron calculations on heteroaromatic systems

The electronic spectra and structures of aromatic monoamino and diamino compounds have been calculated using a modification of the Pariser-Parr-Pople method. Electronic transitions investigated involve singlet-singlet and triplet-triplet - ^* excitations. A limited configuration interaction has been included involving single electron excitations and both single and double electron excitations between the two highest occupied and two lowest unoccupied molecular orbitals. Improvement of oscillator strengths was observed with increasing number of configurations considered. Good agreement was obtained between calculated and experimental molecular ionization potentials.

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Zusammenfassung Mono- und Diaminoaromaten wurden mit der modifizierten PPP-Methode von Adams und Miller untersucht, speziell ihre - ^*-Übergänge und Ionisationspotentiale. CIRechnungen mit einfachangeregten Konfigurationen wie mit einfach und doppeltangeregten Konfigurationen zeigten eine mit der Zahl der Konfigurationen steigende Verbesserung der Oszillatorenstärken.

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Résumé Les spectres électroniques et les structures de composés aromatiques mono et di-aminés ont été calculés en utilisant une variante de la méthode de Pariser-Parr-Pople. Les transitions électroniques étudiées sont les transitions ^* singulet-singulet et triplet-triplet. Une interaction de configurations limitée est introduite en considérant des mono et des di excitations entre les deux plus hautes orbitales moléculaires occupées et les deux plus basses libres. Les forces oscillatrices sont améliorées lorsque le nombre de configurations considérées augmente. Un bon accord est obtenu entre les poteientls d'ionisation moléculaire calculés et expérimentaux.

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This investigation was supported by a National Science Foundation Grant No. GB-4065. Abstracted in part from the Master's thesis of D. R. Forshey, Duquesne University, 1967.     

A comparison of empirical force field parameters for molecular mechanics calculations on saturated hydrocarbons

Nine empirical force fields used in molecular mechanics calculations are tested for their abilities to reproduce experimental geometric and energy data on $\text{cis-syn-cis}$-perhydroanthracene.     

Modified MINDO/3 13C chemical shift calculations for simple hydrocarbons

Calculations of ¹³C chemical shifts in some simple hydrocarbons have been carried out using the GIAO approach in the MINDO/3 semiempirical formalism. In order to achieve reasonable agreement with experiment it is necessary to modify (increase) the vacant orbital energies in the MINDO/3 calculation in order to reduce the magnitude of the paramagnetic contribution, and to also modify this dominant term by generally reducing it as a function of the number of hydrogen and carbon atoms bonded to the resonant nucleus in question. For a set of 34 resonant nuclei of the simpler hydrocarbons, agreement with experiment of the order of 7.8 ppm is attained; however, pathological cases such as cyclopropane and some simple allenes continue to cause problems, increasing the standard deviation of the full set to 12.5 ppm. Our results indicate that the MINDO/3 approach is as viable for ¹³C chemical shift calculations as other semiempirical approaches, all of which seem currently to be limited to a standard deviation of the order of 10 ppm.     

A block variational procedure for the iterative diagonalization of non-Hermitian random-phase approximation matrices

We present a technique for the iterative diagonalization of random-phase approximation (RPA) matrices, which are encountered in the framework of time-dependent density-functional theory (TDDFT) and the Bethe-Salpeter equation. The non-Hermitian character of these matrices does not permit a straightforward application of standard iterative techniques used, i.e., for the diagonalization of ground state Hamiltonians. We first introduce a new block variational principle for RPA matrices. We then develop an algorithm for the simultaneous calculation of multiple eigenvalues and eigenvectors, with convergence and stability properties similar to techniques used to iteratively diagonalize Hermitian matrices. The algorithm is validated for simple systems (Na(2) and Na(4)) and then used to compute multiple low-lying TDDFT excitation energies of the benzene molecule.     

Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation

Two related methods to calculate the Kohn-Sham correlation energy within the framework of the adiabatic-connection fluctuation-dissipation theorem are presented. The required coupling-strength-dependent density-density response functions are calculated within exact-exchange time-dependent density-functional theory, i.e., within time-dependent density-functional response theory using the full frequency-dependent exchange kernel in addition to the Coulomb kernel. The resulting resolution-of-identity exact-exchange random-phase approximation (RI-EXXRPA) methods in contrast to previous EXXRPA methods employ an auxiliary basis set (RI basis set) to improve the computational efficiency, in particular, to reduce the formal scaling of the computational effort with respect to the system size N from N(6) to N(5). Moreover, the presented RI-EXXRPA methods, in contrast to previous ones, do not treat products of occupied times unoccupied orbitals as if they were linearly independent. Finally, terms neglected in previous EXXRPA methods can be included, which leads to a method designated RI-EXXRPA+, while the method without these extra terms is simply referred to as RI-EXXRPA. Both EXXRPA methods are shown to yield total energies, reaction energies of small molecules, and binding energies of noncovalently bonded dimers of a quality that is similar and in some cases even better than that obtained with quantum chemistry methods such as Mo?ller-Plesset perturbation theory of second order (MP2) or with the coupled cluster singles doubles method. In contrast to MP2 and to conventional density-functional methods, the presented RI-EXXRPA methods are able to treat static correlation.     

Electronic structure of saturated hydrocarbons in the semi-empirical equivalent orbital method

The problem of obtaining the matrix elements of Hartree-Fock Hamiltonians for alkanes using the EO method is considered. It has been shown that the data on the electronic structure of diamond together witht ₁/e splitting in the neopentane photoelectron spectrum are helpful to produce such EO method parameter scale which involves even “through space” interactions. In terms of the EO method the photoelectron spectra of propane, butane, isobutane, and neopentane are interpreted. The valence band structure of polyethylene in analytical form is obtained.