Quantum Chemistry Jan. 1994 Vol. 49, No. 2 ============================================ On the Applicability of the Screened-Coulomb Exchange Model in Kohn--Sham Density Functional Studies E. I. PROYNOV* AND D. R. SALAHUB ................. 67 Departement de chimie, Universite de Montreal, C.P. 6128, Succ. A, Montreal, Quebec, H3C 3J7, and Centre de Recherche en Calcul Applique, Montreal, Quebec H3X 2H9, Canada Abstract The screened-Coulomb exchange model used first in the X” method and later on in Kohn--Sham density functional theory is reexamined. Based on the well-elaborated framework of the local spin-density approximation, we show that this model is not well suited when systems with a finite number of electrons are concerned, because it does not respect the pair-density sum rule. A proper modification of the model is proposed by reformulating it in terms of a screened-exchange hole and ensuring the sum rule for this hole. As a result, it is shown how the static screened exchange in finite systems is accompanied by a conjugate antiscreened one. The possible consequences of this effect on the application of the screened-Coulomb exchange model are discussed. 1994 John Wiley & Sons, Inc. ---------------------------------------------------------------- Applications of the Molecular Orbital Graph Theory: A Topological Method to Calculate a_{N-K} Based on a_{N} HONGGANG ZHAO, JIPING LI, SHIXIAN HU, AND JICAI ZHANG ........ 81 Department of Chemistry, Liaoning Normal University, Dalian, People's Republic of China Abstract A formula of the coefficient a_{N-K} of the eigenpolynomials connected with the zero-order term's coefficient of the eigenpolynomials corresponding the k-order-induced subgraph's molecular fragments has been induced. From this formula, a_{N-K} can be calculated and the contributions of the induced subgraph's molecular fragments to the stability and reactivity of the molecules are revealed. 1994 John Wiley & Sons, Inc. ---------------------------------------------------------------- Net Signs of Molecular Graphs: Dependence of Molecular Structure IVAN GUTMAN, SHYI-LONG LEE, YEUNG-LONG LUO, YEONG-NAN YEH .... 87 IVAN GUTMAN Institute of Chemistry, Academia Sinica, Taipei, Taiwan 11529, Republic of China SHYI-LONG LEE* Department of Chemistry, National Chung-Cheng University, Chia- Yi, Taiwan 621, Republic of China YEUNG-LONG LUO Institute of Chemistry, Academia Sinica, Taipei, Taiwan 11529, Republic of China YEONG-NAN YEH Institute of Mathematics, Academia Sinica, Taipei, Taiwan 11529, Republic of China Abstract The concept of internal connectivity associates to each eigenvector of the molecular graph a graph with signed edges. We show that the respective edge signs can be deduced without knowing the graph eigenvectors. The dependence of the edge signs on molecular structure is elucidated. The sign of an edge whose end vertices are v_{r} and v_{s} is found to be the result of separate interactions through all paths connecting the vertices v_{r} and v_{s}. The analysis of the edge signs is particularly simple in the case of acyclic systems. 1994 John Wiley & Sons, Inc. ---------------------------------------------------------------- Energy Levels of Small Titanium Oxide Clusters Obtained from SCF Calculations A. HAGFELDT, S. LUNELL, H. O. G. SIEGBAHN ................. 97 A. HAGFELDT Department of Physical Chemistry, Box 532, and Department of Physics, Box 530, University of Uppsala, S--75121 Uppsala, Sweden S. LUNELL Department of Quantum Chemistry, University of Uppsala, Box 518, S-75120 Uppsala, Sweden H. O. G. SIEGBAHN Department of Physics, University of Uppsala, Box 530, S-75121 Uppsala, Sweden Abstract The energy levels of small titanium oxide clusters [(TiO_{2})_{2}, (TiO_{2})_{3}, and (TiO_{2}H)_{2}] have been calculated using ab initio SCF methods. Both crystal and relaxed geometries have been considered. Systematic changes in the valence-level structure resulting from geometry relaxation are found, which may be related to band-gap changes experimentally observed for small titanium oxide particles. In addition, a Ti--- OH local surface state is found to be well described within a limited cluster model. 1994 John Wiley & Sons, Inc. ---------------------------------------------------------------- Reaction Path as a Gradient Line on a Potential Energy Surface RUSLAN M. MINYAEV ................. 105 Institute of Physical and Organic Chemistry, Rostov State University, Rostov-on-Don, Stachka Ave, 194/3, 344104 Russia Abstract The reaction path is shown to be always a gradient line on a potential energy surface (PES) of a molecule. The properties of gradient lines on the PES are elucidated. Correct symmetry conservation rules along the gradient line are derived. The behavior of the gradient line on a PES with different topologies are considered. 1994 John Wiley & Sons, Inc.