Thomas-Fermi-Dirac calculations for molecules

The electrostatic potential derived from a solution to the molecular Thomas-Fermi-Dirac equation for F₂ is combined with the exchange potential and modified to give the correct behavior far from the nuclei. One-electron energy levels in this potential are calculated and are in qualitative agreement with SCF orbital energies. Similar computations are carried through for F and Ar, which correspond to the separated and united atoms for F₂. To compensate for errors in the potential, we subtract from molecular orbital energies the difference of TFD and SCF orbital energies for the separated atoms. Now all the orbital energies are correct to a few electron volts.

---

Zusammenfassung Das elektrostatische Potential, das sich für F₂ aus der Thomas-Fermi-Dirac Theorie ergibt, wird mit dem Austauschpotential kombiniert und so modifiziert, daß sich das richtige Verhalten in Kernnähe ergibt. Die berechneten Einelektronenenergien sind in qualitativer Übereinstimmung mit SCF-Werten. Analoge Rechnungen für F und Ar werden ausgeführt und als Grenzfälle für Korrekturen verwendet. Dann ergeben sich alle Orbitalenergien bis auf wenige eV richtig.

---

---

Supported by the National Science Foundation under Grant GP-20718.     

PPP and CNDO calculations for protonated molecules

CNDO calculations have been used to obtain the one-centre core integrals for protonated azines required in calculating the ^* absorption spectra of such molecules using the PPP method. Calculated spectra for both the parent and the protonated molecules are obtained in satisfactory agreement with experiment. The changes in the -framework of the molecules on protonation are also discussed in terms of the CNDO results.

---

Zusammenfassung CNDO-Rechnungen wurden benutzt, um die Einzentren-Rumpf-Integrale für protonierte Azine zu erhalten, die bei der Berechnung der ^* -Absorptionsspektren mit Hilfe der PPP-Methode benötigt werden.Die berechneten Spektren für die Ausgangsmoleküle und die protonierten Moleküle sind in zufriedenstellender Übereinstimmung mit dem Experiment. Die Veränderungen im -Rumpf der Moleküle bei der Protonierung werden ebenfalls mit Hilfe der CNDO-Resultate diskutiert.

---

Résumé Des CNDO ont tét utilisés pour obtenir les intégrales de coeur monocentriques des azines protonées nécessaires au calcul de leur spectre d'absorption ^* par la méthode PPP. Les spectres calculés pour les molécules protonées ou non sont en accord satisfaisant avec l'expérience. Les modifications subies lors de la protonation par le squelette sont discutées en fonction des résultats des calculs CNDO.

     

A new program for CI calculations in molecules

Based on the formalism developed in a recent note, we have worked out a program for CI calculations in molecules. In the present note, the details of the program are discussed. The usefulness of the program has been illustrated using some calculations. On leave from the Indian Institute of Technology, Bombay, India.     

Resonance Raman scattering amplitude calculations for diatomic molecules

A direct procedure for calculating resonance Raman scattering amplitudes for diatomic molecules is presented and compared with other calculational procedures. An extension of the present procedure is outlined for cases where there is more than one excited intermediate state and these states interact with one another.     

Ground states of molecules. 56. MNDO calculations for molecules containing sulfur

MNDO has been extended to sulfur, but without inclusion of 3d AO s. Calculations are reported for heats of formation, geometries, dipole moments, and ionization energies of a variety of sulfur-containing molecules. The average discrepancy between calculated and observed heats of formation is larger than for compounds of other elements, a difference probably due, at least partly, to the lower accuracy of the thermochemical data for sulfur compounds. The calculated dipole moments agree well with experiment as do the calculated ionization energies, except for those corresponding to ionization from sulfur “lone-pair” orbitals which are too high by ca. 1 eV, probably as a result of the neglect in NDDO of interactions between inner and valence shell orbitals. As in the case of other third-period elements, the calculated heats of formation of compounds of sulfur in its higher valence states (S^IV, S^VI) were too positive by large amounts, due presumably to the neglect of 3d AO s.     

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.     

CEPA calculations on open-shell molecules

Ab initio calculations at SCF and CEPA levels using large Gaussian basis sets have been performed for the two lowest electronic states,X ² Σ⁺ andA ² Π, of HeAr⁺. Spin-orbit coupling (SOC) effects have been added using a semiempirical treatment. The resulting potential curves for the three statesX,A ₁, andA ₂ have been used to evaluate molecular constants such as vibrational intervals ΔG(v + 1/2) and rotational constantsB _v as well as — by means of a Dunham expansion — equilibrium constants such asR _e , ω _e ,B _e etc. Comparison with the experimental data from UV emission spectroscopy shows that the calculated potential curves are slightly too shallow and have too large equilibrium distances:D _e = 242 cm^?1 andR _e = 2.66 Å compared to the experimental values of 262 cm^?1 and 2.585 Å, respectively, for theX ²Σ⁺ ground state. However, the ab initio calculations yield more bound vibrational levels than observed experimentally and allow for a more complete Dunham analysis, in particular for theA ₂ state. The experimental value of 154 cm^?1 for the dissociation energyD _e of this state is certainly too low; our best estimate is 180±5 cm^?1. For theA ₁ state our calculations are predictions since this state has not yet been observed experimentally.     

Valence-shell calculations on polyatomic molecules

Calculations using the CNDO/2, the Extended Hückel (EH) method, and an iterative Extended Hückel (IEH) method are reported for HF, H₂O, NH₃, CO, H₂CO, HCONH₂, HCOOH, HCOF and sydnone. For the IEH method, it is shown that if the dipole moment is calculated by including the atomic dipole moment and the overlap moment (homopolar dipole) as well as the term from the Mulliken populations, then, except for carbon monoxide, the IEH method gives results in good agreement with experiment. The non-iterative EH method predicts dipole moments that are much too high. For molecules with dipole moments smaller than 3 Debyes, the IEH and CNDO/2 methods give similar results, but for molecules with higher dipole moments (formamide and sydnone), the CNDO/2 method gives better agreement with experiment. Comparison of the calculations on sydnone with those on other carbonyl compounds suggests that sydnone is best represented as a resonance stabilized azo-methine imine rather than as a meso-ionic or betaine type compound.

---

Zusammenfassung Rechnungen mittels des CNDO/2- und des erweiterten Hückelverfahrens (iterativ und nichtiterativ) werden für HF, H₂O, NH₃, CO, H₂CO, HCONH₂, HCOOH, HCOF und Sydnon vorgelegt. Im Fall des iterativen Hückelverfahrens zeigt sich, daß die Dipolmomente (außer für CO) gut mit dem Experiment übereinstimmen, wenn man die atomaren Dipol- und die Überlappungsmomente sowie die Terme der Mulliken-Population berücksichtigt. Dagegen sind die entsprechenden Werte des nichtiterativen Verfahrens viel zu groß. Für Moleküle mit Dipolmomenten kleiner als 3 Debye liefert das CNDO/2-Verfahren ähnliche Werte wie die iterative Hückelmethode, für Moleküle mit größeren Dipolmomenten dagegen bessere Resultate. Vergleicht man die Rechnungen für Sydnon mit denen für andere Carbonylverbindungen, so scheint es, daß man es besser als resonanzstabilisiertes Azomethinimin und nicht als Betain auffassen sollte.

---

Résumé HF, H₂O, NH₃, CO, H₂CO, HCONH₂, HCOOH, HCOF et la Sydnone on été calculées en utilisant les méthodes CNDO/2, Hückel étendu (EH) et Hückel étendu itératif (IEH). On montre que, pour la méthode IEH, si l'on calcule le moment dipolaire en incluant le moment dipolaire atomique et le moment de recouvrement (dipôle homopolaire) ainsi que le terme provenant des populations de Mulliken, les résultats obtenus sont en bon accord avec l'expérience sauf pour l'oxyde de carbone. La méthode EH non itérative donne des moments dipolaires trop élevés. Pour les molécules de moment inférieur à 3 Debyes, IEH et CNDO/2 donnent des résultats similaires, mais pour les molécules à moments plus élevés (formamide et sydnone) la méthode CNDO/2 donne un meilleur accord avec l'expérience. La comparaison des calculs sur la sydnone avec ceux sur les autres composés carbonylés suggère que la sydnone est mieux représentée comme une azo-méthine imine stabilisée par résonance que comme un composé de type «méso-ionique» ou bétaïnique.

---

---

This work was supported by Grant No. MH-12951-02 from the National Institutes of Health, Bethesda, Maryland, USA.

---

NASA Research Trainee.     

Generalized Bethe-Goldstone calculations on molecules

Computer programs have been developed in order to apply Nesbet's method of generalized Bethe-Goldstone equations to the calculation of electronic correlation effects in molecules. After an outline of the method some preliminary results for H₂O and BH are presented.     

Relativistic Dirac–Fock calculations for closed-shell molecules

A new code has been written to perform relativistic Dirac–Fock self-consistent field (SCF) calculations on closed-shell molecules of any symmetry. The choice of the basis set allows us to work at different levels of approximation depending on the precision required. Calculations on the H₂Po molecule show that accurate results on specific problems like geometry optimization can be obtained by evaluating the two-electron integrals on half the basis spinors. © 1994 by John Wiley & Sons, Inc.     

An unconventional scf method for calculations on large molecules

An unconventional SCF method for calculations on large molecules with more than 100 basis functions is described. Storage problems which arise in conventional SCF schemes when storing more than 10⁷ integrals are avoided by repeated calculation of integrals. The resulting increase in computational times is kept at a reasonable level by (a) improving the initial guess, (b) accelerating convergence, (c) employing a recursive construction of the Fock matrix, and (d) eliminating insignificant integrals from the calculation by a density-weighted cutoff criterion. Sample calculations show that, compared with conventional SCF calculations, computational times increase by 25%–75% depending on the basis set and the shape of the molecule.     

Using many-particle basis sets for electronic energy calculations of molecules

A method of calculating the electronic energies of molecules using a many-particle basis set is proposed. In this case, the many-particle Schrödinger equation may be solved without resorting to the one-electron approximation. The results of the electronic energy calculations of some two-electron systems are in good agreement with experimental results.     

Molecules in molecules calculations on decacyclene

The calculation of the ring-current contribution to the proton chemical shifts in conjugated systems using uncoupled Hartree-Fock perturbation theory is improved by the inclusion of origin variation in the expression for the vector potential.     

Valence shell calculations on polyatomic molecules

Dipole moments and charge distributions for twenty molecules of widely different types have been calculated using (a) the CNDO/2 method and (b) a CNDO/2D method in which the orbitals from the CNDO/2 method are deorthogonalized by a Löwdin transformation and are then used to calculate the dipole moments in a rigorous manner. A statistical analysis of the results for the dipole moments calculated by the CNDO/2D method shows that they are in very slightly better agreement with experiment than those from the CNDO/2 method. The net charge distributions from the CNDO/2D method follow more closely the trends of ab initio calculations than do the CNDO/2 net charges.

---

Zusammenfassung Dipolmomente und Ladungsdichten von Molekülen unterschiedlichen Typs wurden mittels des CNDO/2- und CNDO/2D-Verfahrens (d. i. mit delokalisierten Löwdin-Orbitalen als AO's) berechnet. Eine statistische Analyse zeigt, daß die Resultate der zweiten Methode etwas besser als die der ersten den experimentellen Ergebnissen folgen. Das Analoge gilt für die Nettoladungsverteilungen in bezug auf die Trends bei ab initio-Rechnungen.

---

Résumé Les moments dipolaires et les distributions de charge pour vingt molécules de types divers ont été calculés par: a) la méthode CNDO/2; b) une méthode CNDO/2D où les orbitales de CNDO/2 sont déorthogonalisées par une transformation de Löwdin. Une analyse statistique montre que les moments dipolaires calculés par CNDO/2D sont légèrement en meilleur accord avec l'expérience que ceux calculés par CNDO/2. Les distributions de charge de CNDO/2D sont plus ressemblantes à celles de calculs ab-initio que ne le sont les distributions de CNDO/2.

---

---

This work represents part of the Ph.D. Dissertation submitted to the University of Virginia by D. D. S. and was supported by Grants No. 1-F01-GM41986-01 from the National Institutes of Health, Bethesda, Maryland, U.S.A., and No. AF-AFOSR-1184-67 from the Air Force Directorate of Scientific Research.

---

NASA Research Trainee.     

Conformation calculations on strained aromatic molecules

Interaction potentials for unconnected atoms are refined, together with the elastic constants needed to calculate conformations for strained molecules from the mechanical model. Equilibrium configurations are derived for octachloronaphthalene, 1, 4, 5, 8-tetrabromonaphthalene, 3, 5-dichloroanthracene, benzene halides, 2, 2-paracyclophane, diphenyl, and 5, 6-dichloro-11, 12-diphenylnaphthacene. The results agree satisfactorily with experiment. It is concluded that the model allows interpretation and a priori prediction of conformations for strained aromatic systems.