Optimization of virtual orbitals in the framework of a multiconfiguration spin-coupled wave function

A new method is introduced for the optimization of nonorthogonal virtual orbitals for use in general multiconfiguration spin-coupled wave functions. The use of a number of highly effective approximations greatly reduces the computational effort involved, the most important being the use of a second-order perturbation expression for the energy and an approximate expression for the elements of the Hessian. As a result, the overall scheme scales very favourably with respect to the numbers of active electrons and of basis functions, making it suitable for the accurate study of large systems. Benchmark calculations are presented for the dissociation of LiH(X¹Σ⁺) and Li₂(X¹Σ⁺ _g ) using a highly compact four-configuration wave function. Standard spin-coupled valence bond expansions in the same virtual space are required to be significantly larger before equivalent results are obtained. The results are shown to compare very favourably with full valence complete active space self-consistent field calculations using an identical basis, and binding energies are within 4% of the values obtained from full configuration interaction calculations in the same basis set. Received: 10 June 1997 / Accepted: 7 October 1997     

An analysis of the polarizabilities in some conjugated molecules

Atom-atom, atom-bond and bond-bond polarizabilities are calculated with a previously used LCAO approximation. Some properties of naphtalene, assumed as general for alternant hydrocarbons, seem to depend on the approximation employed. Atom-atom polarizabilities in azines are related to other theoretical and experimental quantities. In all the molecules studied, the part played by formal bonds is highly stressed.

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Zusammenfassung Atom-Atom-, Atom-Bindungs- und Bindungs-Bindungs-Polarisierbarkeiten werden mit einem schon früher benutzten LCAO-Verfahren berechnet. Einige Eigenschaften von Naphthalin, die für alternierende Kohlenwasserstoffe als charakteristisch angesehen werden, scheinen von der benutzten Näherung abzuhängen. Atom-Atom-Polarisierbarkeiten in Azinen werden auf andere theoretische und experimentelle Größen zurückgeführt. In allen betrachteten Molekülen spielen formale Bindungen eine bedeutende Rolle.

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Résumé Calcul des polarisabilités atome-atome, atome-liaison et liaison-liaison dans une approximation LCAO utilisée auparavant. Certaines propriétés du naphtalène, supposées générales pour les hydrocarbures alternants, semblent dépendre de l'approximation employée. Les polarisabilités atome-atome des azines sont reliées à d'autres grandeurs théoriques et expérimentales. Dans toutes les molécules étudiées, le rôle joué par les liaisons formelles est mis en relief.

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With a fellowship from the Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina.

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With a fellowship from the Centro Latino Amerioano de Física.

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The authors gratefully acknowledge the helpful discussions with Dr. J. Brieux and Lic. H. C. González, who has besides collaborated in part of the calculations.     

Role of entropy in increased rates of intramolecular reactions

The rates of intramolecular condensation of a series of monoesters of dicarboxylic acids have been shown to be highly dependent on the nature of the intervening groups. To understand the origin of this effect, we estimated DeltaS(NAC,S), the entropy difference between the ensemble of accessible ground state conformers and a single ground state conformer having transition-state-like geometry. DeltaS(NAC,S) differs from the activation entropy for the reaction by DeltaS(TS,NAC), the difference in vibrational entropy between the selected ground state conformer and the transition state. The estimated values of DeltaS(NAC,S) correlate well (R(2) = 0.96 and 0.73 using dielectric constant values of 80 and 1, respectively) with experimentally determined reaction rate constants. Normal-mode analysis performed on minimized ground state conformations of each molecule suggests that the change in vibrational entropy makes only a small contribution to the total activation entropy. These results indicate that the conformational entropy difference between the transition and the ground states contributes significantly to the free energy of activation.     

Structure of the larvicideN-(2-chlorobenzoyl)-N′-[4-(2-chloro-3,3,3-trifluoroprop-1-enyl)phenyl]urea,C17H11Cl2F3O2N2

Mw=403,2 amu,P2₁/c,a 18.944(8) Å,b=8.540(4) Å,c=10.794(7) Å,=98.11(4)°,V=1729(2) ų,Z=4,D _x=1.548 g·cm^–3, (MoK)=4.26 cm^–1; m.p. 202–204°C. FinalR=0.083 for 1632 independent observed reflections having 2 (Mo K)<50° andI>2 (I). The molecule has an extended overall nonplanar conformation with onecis and twotrans-C(O)-NH- units and intramolecular hydrogen bridges. The relatively highR factor is on account of conformational disorder of the trifluoromethyl and chloro substituents of the 2-chloro-3,3,3-trifluoropropenyl moiety.     

On two conjectures about Dennis-Moré conditions

Numerical Algorithms - Quasi-Newton methods for solving nonlinear systems of equations are generally defined in order to satisfy a “direct secant equation” or an “inverse secant...     

Labelling of Carbaboranyl Compounds with a Selenium Atom with a View to Applications in Boron‐Neutron‐Capture Therapy (BNCT) and Positron‐Emission Tomography (PET)

We synthesized 2′‐carbaboranyl‐2,5′‐bi‐1H‐benzimidazoles containing 10 B‐atoms and labeled with Se or the positron‐emitting radionuclide ⁷³Se (t_1/2=7.1 h), with a view to their application to cancer treatment by boron‐neutron‐capture therapy (BNCT) and to compound‐distribution measurements in vivo by positron‐emission tomography (PET). Thus, 2,2′‐{{2′‐{4‐[1,2‐dicarba‐closo‐dodecaboran(12)‐2‐ylmethoxy]phenyl}‐[2,5′‐bi‐1H‐benzimidazol]‐5‐yl}imino}bis[ethanol] ( 26c ) was obtained by the reaction of 2,2′‐[(3,4‐diaminophenyl)imino]bis[ethanol] ( 19 ) with ethyl 2‐{4‐[1,2‐dicarba‐closo‐dodecaboran(12)‐2‐ylmethoxy]phenyl}‐1H‐benzimidazole‐5‐carboximidate hydrochloride ( 25 ), as well as the analogues 26a and 26b (Scheme 6). Tosylation of compound 26c gave 4 regioisomers 27a – d , which, after selenation, produced 2′‐{4‐[1,2‐dicarba‐closo‐dodecaboran(12)‐2‐ylmethoxy]phenyl}‐5‐(tetrahydro‐2H‐1,4‐selenazin‐4‐yl)‐2,5′‐bi‐1H‐benzimidazole ( 29 ) in 42% yield (Scheme 7).     

Electrostatic medium effects and formal quantum structure–activity relationships in apomorphines interacting with D1 and D2 dopamine receptors

The binding of apomorphines (AM) to D₁ and D₂ dopamine receptors is analyzed through a formal quantum structure–activity relationship method. The calculations were carried out at the CNDO/2 level of the molecular orbital theory with a continuum representation of environmental effects. The results show that the D₁ receptor affinity variation is related to the variation of the electron-donating capacity of a C atom of the hydroxylic region of apomorphines in a low-polarity medium. The N-chain probably interacts with a hydrophobic region of the receptor. It is also concluded that the poor results for the D₂ binding affinity are explained by errors in the experimental measurements. Finally, it is proposed that future structure–activity relationship studies must be carried out for media of different polarities. © 1997 John Wiley & Sons, Inc.     

Thiolate-Bridged Diiron(III) Complex with Spin-Crossover Behaviour

The reaction of the ligand HL · (HCl)₂ (HL = 2,6-di(aminomethyl)-4-tert-butyl-thiophenol) with MCl₂ in methanol in the presence of sodium methanolate and air affords the dinuclear complexes [L₃M₂][ClO₄]₃ (M = Fe: 2 , Co: 3 ) in 85% and 68% yield, respectively. Both complexes were characterized by infrared spectroscopy, magnetic susceptibility measurements, and ¹H NMR spectroscopy. By temperature-variable ⁵⁷Fe Mössbauer spectroscopy diamagnetic 2 is shown to exhibit a gradual spin transition between the species [L₃(low-spin-Fe)₂]³⁺ ((ls,ls)- 2 ) and [L₃(high-spin-Fe)₂]³⁺ ((hs,hs)- 2 ). At room temperature the relative concentrations of both species are nearly equal. Well resolved quadrupole doublets at all temperatures for both (ls,ls)- 2 (γ in the range 0.22(1)–0.28(1) mm s^–1) and (hs,hs)- 2 (γ in the range 0.48(1)–0.53(2) mm s^–1) are indicative of a spin conversion time longer than the half-life of the I = ³/₂ state of ⁵⁷Fe. Cyclic voltammetry and square wave voltammetry of 2 in CH₃CN solution reveal four quasi-reversible one-electron transfer processes. The first two processes were assigned to metal-centered reductions of (hs,hs)- 2 and (ls,ls)- 2 , respectively, to yield the mixed-valent species [L₃Fe^IIFe^III]³⁺.