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Notes: The optical spectrum of a model oxyheme complex has been calculated using a new intermediate neglect of differential overlap (INDO-SCF-CI) method that allows for the inclusion of configuration interaction and transition metals. In addition to the porphyrin π→π* transitions common to all heme proteins, four weak x,y polarized transitions observed only in oxyheme complexes have been calculated and assigned to excitations involving the lowest-empty highly delocalized (Oπ, dπ) orbital. Two broad z-polarized bands observed in the single-crystal polarized absorption spectra of oxymyoglobin and hemoglobin have also been calculated. Controversy exists over the assignment of these transitions and, in particular, over the extent of involvement of the oxygen ligand. Our calculations assign the weaker near-IR visible band mainly to the d σ dπ→ dπ* excitations and the more intense UV band mainly to a2u → dσ* excitations. While significant participation (25%) of the highly delocalized (Oπ, dπ) virtual orbital is also found, these z-polarized transitions need not be totally unique to oxyheme complexes, in keeping with experimental observation.

Notes: Monoalkyl and dialkyl quarternary ammonium salt-type cationic surfactants containing a phenoxy group as aromatic chromophores at different positions of alkyl chains were synthesized. Monoalkyl-type surfactants formed micelles in aqueous solutions. The bilayer structure similar to that found in phospholipid liposomes was obtained in the aqueous dispersions of dialkyl-type surfactants. The phenoxy groups were partially oriented and aligned in these molecular assemblies. The interactions of aligned phenoxy groups in micelles or bilayers resulted in luminescence with lower energy than that of the monomer fluorescence or in a radiationless deactivation of excited states. Such interactions could be effectively prevented in bilayer structures composed of surfactant molecules containing a “spacer chain” between aligned chromophores. Evidence was obtained supporting energy migrations between aligned chromophores that were separated by a dodecyl chain in the bilayer structure.

Notes: Solvent effects and pH effects on CD and MCD spectra of phenylalanine and its derivatives were observed. CD spectra of N-acetyl-L-phenylalanine ethyl ester in various solvents were analyzed using the rotamer population determined by NMR. The magnitude of optical activity due to each rotamer was determined for two CD bands. The signs of Cotton effect of rotamers I and II are positive and that of rotamer II is negative. The optical activity is greater in polar than in nonpolar solvents. MCD spectra of phenylalanine reveal a remarkable pH effect. In the alkaline pH range it is of the toluene type, from which it turns to a weak spectrum in the acid pH range.

Notes: The properties of V-coupling coefficients from SO(3) to the octahedral group are discussed and, for the purpose of practical use in ligand field theory, the numerical values from j = 1/2 to j = 12 1/2 have been worked out through an Elliott-503 computer. The values for j ≤ 4 1/2 are listed.

Notes: This paper outlines a model for calculating the localized states of a 〈 100 〈 edge dislocation in α-Fe. The model used for the calculations is based on the multiple-scattering model (SCF-X α-SW). The purpose of this research is twofold: (1) To determine changes in electronic structure of the lattice near the core region of defects in α-Fe. (2) The variations of hydrostatic pressure about an edge dislocation produce a rearrangement of the conduction electrons. The question is what electrical interaction might be expected between a dislocation and a charged solute atom. The calculations show that the electrons tend to flow away from the compression side toward the dilated regions. The electrical contribution to the binding energy of a solute atom and a dislocation in α-Fe is of the order of 0.01 Ry/electronic unit charge of the atom.

Notes: The correlation energies obtained by the fourth-order diagrammatic perturbation theory were analyzed for three diatomic molecules: N2, CO, and F2. The results were compared with correlation energies obtained previously for the ten-electron hydrides HF, H2O, and NH3. The relative importance of contributions which arise from the double excitations, from the quadruple excitations, as well as from the renormalization term was investigated. It is shown that for the diatomic molecules under study these contributions are considerably larger than for the ten-electron hydrides not only in absolute value but also in percentage: they represent about 3, 3, and 5%, respectively, of the valence shell correlation energy obtained by the perturbation theory up to the fourth order. A careful analysis of the fourth-order correlation effects is also presented for the reaction energy of the process ½H2 + ½F2 = HF.

Notes: The one-center expansion (OCE) method is extended to evaluate molecular wave functions for molecules with heavy off-center nuclei. This extension is achieved through the use of model potentials (MP) to approximate the highly bound core orbitals. The remaining diffuse valence charge distribution is then rather easy to simulate using OCE. The formulation of the method is described. New molecular integrals are solved to a high degree of accuracy. Successful results are reported for H2O, H2S, and N2. The valence electron distributions and orbital energies are in good agreement with those obtained from more complete calculations. The method combines the computational economy of both OCE and MP procedures, resulting in a potentially useful package for further chemical applications.

Notes: The ground state and the first few excited states of an MnO69- cluster are calculated in the unrestricted Hartree-Fock model. The state ordering is 5B1 g, 5A1 g, 5B2 g, and 5Eg as can be expected from simpler models. Consistent with the results by the same method for copper complexes, we obtain d-d transition energies about one half or less of the experimental energies. The charge transfer spectrum is subject to a large spin polarization in the sense that the lowest charge transfer state (5Eu) has five unpaired spins on Mn.

Notes: A theoretical order-disorder model for the main phase transition of lipid monolayers is presented here. The model contains approximate treatments of hard-core repulsions and attractive forces between molecules. The lipid molecules are assumed as the square plates and then the entropy of the configurations is obtained using the placement method in a two-dimensional lattice. The approximation used to compute the thermodynamic behavior of the model turns out to be a kind of molecular-field approximation. The resultant pressure-density isotherms for the three-state model show the characteristic van der Waals loops.

Notes: The optimality of MO basis sets of Gaussian functions, when constructed from AO basis sets optimized for the neutral atom or for atom ions, is investigated. A formal charge parameter Q is defined and used to adjust the AO basis sets to the molecular environment, by virtue of a simple quadratic expression. Calculations on a series of C1 hydrocarbons (CH2, CH3, CH3+, CH3-, CH4) using 3G basis sets indicate considerable variations in the optimum Q value with the molecular species. The proposed method offers a simple alternative technique to a full molecular basis set optimization.

Notes: It is shown that the treatment of the superexchange in insulators, based on the spin projected extended Hartree-Fock (EHF) method may be considered as a direct generalization of Anderson's ligand field (or kinetic exchange) theory: the EHF methods permits to construct explicitly the effective orbitals for the magnetic electrons and to determine all the parameters occurring in Anderson's theory from only one variational problem.

Notes: The electrostatic interaction for arbitrary symmetry (including non-simply reducible point groups), different coupling schemes, and several open shells is discussed from a common viewpoint using the particle-number representation (second quantization). The different coupling schemes simply arise from a different interpretation of the relevant symmetry group. Using the adjective CFPS of the preceding paper, the interaction within several open shells can be calculated. In the case of one-center expansions like ligand field theory the many-particle matrix elements are directly expressed by the radial Slater integrals using isoscalar factors. An example of the formalism is worked out. By the way the unitary transformations between strong and weak field coupling schemes are expressed recursively in the number of particles.

Notes: Variable electronegativity Pariser-Parr-Pople (VE-PPP) calculations have been carried out on the bases of nucleic acids and 5-fluorouracil. Directions of polarization for the various electronic transitions in these molecules have been calculated using the wave functions obtained by this and the CNDO/S-CI methods. The calculated excitation energies, oscillator strengths, and directions of polarization have been compared with the PPP results due to Pullman and co-workers and Bailey as well as the experimental ones. It has been found that a comparative study of this type is much more useful for understanding the transitions in the molecules than the individual calculations. The VE-PPP method is found to generally give the best results. The directions of polarization have been used to identify the transitions in the molecules and to compare the excitation energies obtained by different methods. It is shown that the transitions in these molecules do not have the characteristics of those of benzene derivatives. All the observed peaks in the molecules have been explained as π*→π.

Notes: The salient features of generalized second-quantization representations for nonrelativistic systems of composite particles are reviewed and their application to a reformulation of the quantum theory of reactive collisions is discussed. Such representations allow the properties of the bound composite states to be built explicitly into the algebra of states and observables. A single unperturbed Hamiltonian simultaneously describes the free propagation of the various species of bound composites as well as of their unbound constituents, while the interaction Hamiltonian describes only true scattering and reaction processes. The inclusion of the binding of all composites in the unperturbed Hamiltonian cures the divergences in the Born series arising from bound-state poles. Unstable composites can be included in a natural way, leading to an explicit representation for the kinematics and dynamics of their decay and their contribution to collision phenomena.

Notes: The fundamentals of the theory of density matrices are reviewed. The density matrix is introduced first in terms of state vectors for pure states over which a probability distribution is given. It is then shown that the applications of the density matrix do not require knowledge of the particular probability distribution over pure states that may have been used for its original determination. It is stressed that density matrices, like state vectors, describe ensembles rather than single systems, as determinism in quantum theory (except for some conservation laws) is of a statistical character only. The entropy of a quantum-mechanical system is defined as the average per system of the entropy of an ensemble of systems described by the quantum-mechanical (pure or mixed) state. For pure states this entropy is zero, in agreement with the fact that state vectors constitute the maximal information that can be given about a quantum-mechanical system. As the entropy should be independent of the particular probability distribution over pure states that may have been used to form the mixed state, it is calculated from statistical considerations about an imaginary ensemble in which the eigenvalues of the density matrix are probabilities over pure states given by the eigenfunctions of the density matrix. The entropy is calculated for a mixture of two nonorthogonal states. The time evolution of the density matrix, in general, is not a unitary transformation, as observable systems are not closed and therefore in the Hamiltonian contain unknown external parameters that are not the same for the entire mixture. Therefore transitions between pure states and mixed states take place. Those from pure to mixed states take place spontaneously and irreversibly under increase of entropy. Transitions from mixed states to pure states can be fabricated; an example is given. As Wigner's thought experiment of mixing coherently the two beams from a Stern-Gerlach apparatus according to estimates of Bohm should be impossible by loss of coherence in the gradient magnetic field, it is indicated how Wigner's ideas may be realized by using, instead, polarized light beams from birefringent crystals. After a brief review of the quantum theory of measurements and the various arguments usually given for the reducibility of state after the measurement, Wigner's argument against blind use of these arguments is interpreted as a limit of validity of the familiar probability rule of quantum theory, which should not be applied after an unsuccessful measurement. By splitting light beams coherently by glass plates, one can by the same apparatus have measurements both of the relative intensities of two coherent beams, and of interference effects between the two beams. This shows that complementarity applies to the individual systems in the beam, as they reach the glass plate where a choice must be made between two complementary possibilities of future measurement. Finally, by describing Schrödinger's cat by a density matrix and asking about its time dependence, it is shown that, if it were possible to measure the interference effects between living and dead cats used by some people as a justification for writing down a state vector for the cat, then this measurement could be used to revive some dead cats.

Notes: This paper proposes a direct, quantum-mechanical definition for Γ (effective action) using a two-step procedure for applying the variational principle to time-dependent quantum problems.

Notes: By using quantum-field theory techniques and the boson transformation method, we study systems that exhibit macroscopic ordered states. As an illustration, we apply the method to the study of superconducting systems by taking into account the quantization of the vector potential. The results of a dynamical calculation, performed in the pair approximation, are presented. The Higgs phenomenon is also discussed in the framework of a fully quantum theory.

Notes: Some aspects of fiber bundles, sheaf theory, and possible generalizations of the notion of differentiable manifolds are discussed.

Notes: Relativistic quantum-field theory provides the machinery for calculating wave functions or probability amplitudes depending upon space-time coordinates. The currently accepted theory, however, fails to provide position operators and a means of measuring particle coordinates that are consistent with Dirac's properties of physical observables. This is because it calls for a space position probability distribution at a specified time. This paper shows, however, that space-time event coordinate operators, together with a corresponding measurement procedure, can be found that are consistent with Dirac's requirements. This is done through a reinterpretation of the amplitudes computed by field theory and does not involve any change in that mathematical formalism. The measurement of the space-time coordinates of an event is accomplished by detecting the absorption of a photon by a particle from each of two light pulses designed to overlap at a given point at a given time. If a final emitted photon has an energy whose sum with the final particle energy approximately equals the sum of the mean energies of the pulses, then the absorption of the two pulse photons must certainly have taken place within a distance the order of a Compton wavelength of the small space-time region of overlapping pulses. This is clear from the fact that the high energy required to confine the pulses to very small volumes must throw a particle absorbing them far off the mass shell. Thus the absorption of the two photons throws the particle into a narrowly confined spatial wave function that must decay extremely rapidly - to within a Compton wavelength, a delta function in space-time. This delta function is the eigenfunction of space-time coordinate operators Xμ and is the scalar product of vectors in a Hilbert space spanned by spin-space-time kets large enough to contain the operators of the Poincaré group. These event operators transform properly under the action of Poincaré operators but do not commute with the mass. If the Compton wavelength is not negligible compared to the accuracy desired in the coordinate measurements, individual coordinate measurements are no longer possible. Nevertheless, a large number of repeated coordinate measurements can be carried out to produce a coordinate probability distribution. This distribution can be unfolded to find a true coordinate probability distribution if the charge form factor is known from basic theory. An analysis of laboratory particle detection techniques shows that they actually determine space coordinates and energy rather than spatial coordinates at a given time. When this fact is included, the Klein-Nishina formula can be derived using the electromagnetic four-vector potential as the photon probability amplitude wave. To clarify the meaning of the observables, a mass-momentum measurement is described.

Notes: Let two strongly continuous one-parameter semigroups of contraction operators, {Z(t); t≧ 0} and {Z0(t); t ≧ 0}, determine physical evolutions realized in the Hilbert spaces ℋ and ℋ0, respectively. We consider the mappings under Z(t) and Z0(t), when the infinitesimal generators G and G0 belong to a product class, properly defined with respect to an H0-norm. The inversed transform of each side in the identity R(λ, G) = R(λ, -iH0)-iR(λ, -iH0)VR(λ, G), which represents a simple algebraic decomposition of the resolvent of G, converges on Ψ if and only if Ψ ∊ D(G). By iteration an asymptotic series emerges, when t → 0. Numerical considerations of this approximation in its first order may support the form of a deviation from the pure exponential decay when the semigroup is compared with a integral transform corresponding to a certain self-adjoint H0 in ℋ0. The deviation may hardly ever be observed and it is therefore most fruitful to discuss the results inside the framework of the enveloping algebra of the semigroups.

Notes: The nodes where the wave function changes sign in conventional quantum theory can alternatively be regarded as places where the wave function descends to zero but rises again without changing its sign. This behavior is accomplished by adding delta function barriers to the potential energy wherever a node occurs in the wave function. This model is supported by the recognition that the wave functions of a subsystem, which is not truly isolated, are really marginal amplitudes which implicitly average out interactions of the system with its environment. The finite effect of these interactions is to replace the delta function barriers by barriers of finite width and height.

Notes: A formulation of quantum mechanics is presented based on the theory of semigroups and the associated enveloping algebras of functions defined on countable subsemigroups. The existence of a unique *-involution is not assumed. The fundamental elements of a semigroup are identified with experimental precedures for the separation of subensembles from a given ensemble of experimental systems. Observables are represented as elements of enveloping algebras, and ensembles as density matrices within an enveloping algebra. The statistical properties of ensembles are expressed in terms of traces defined on the semigroup and its enveloping algebras. The elements and generators of the Poincaré group can be defined and interpreted in the usual way. A variety of applications is described, in which the theory of the density matrix plays an essential or effective role. Advantages associated with the resulting freedom from the limitations of Hilbert space are illustrated.

Notes: This paper contains the skeleton of one lecture, and of two raporteur's interventions, made at the Sanibel Symposium in February-March, 1979. The task asked of this lecturer was to present an outline of the program of nonequilibrium statistical mechanics, and to indicate some of the recent developments in our understanding of this program. Section I lists a few of the principal physical ingredients of the theory. The possible implementation of certain aspects of the program is demonstrated in Sec. II with the help of three exactly soluble models. Finally in Sec. III we extrapolate from these particular examples in two directions: the stochastic aspect of statistical mechanics, and some remarks on the theory of the quantum measurement process. The presence, at the Symposium, of several distinguished lecturers who presented their own original, and most interesting, contributions hopefully made appear less outrageous - at least at the time - the severe omissions due to the personal choices this particular speaker had to make to keep within the time limitations inherent to such a gathering. It is now hoped that, even when taken out of the full context of the Symposium, the rearranged text which follows might nevertheless help focusing attention on some of the important problems remaining to be solved. It is a pleasure to acknowledge here the stimulating hospitality of the Symposium Scientific Director, Professor P.-O. Löwdin.

Notes: Among the tensors used in the published literature to characterize a phenomenon of nonlinear optics, some are not invariant under a change of origin. In this paper, we show that this invariance can be obtained in a general manner, if the densities of electric and magnetic polarization are not separated but replaced by a density of magnetoelectric polarization whose quantum calculation is performed for a molecular crystal.

Notes: In the previous paper, a global tensor invariant under origin changes was introduced for all optical phenomena. By applying the results obtained, we determine invariant partial tensors which characterize refraction and the Faraday effect.

Notes: A systematic analysis of a diabatization method proposed in a recent publication is presented for the one-dimensional linear model of nonadiabatic transitions, and the method is extended to the exponential model. The asymptotic behavior of molecular properties is studied, and the usefulness of simple properties like the kinetic energy and multipole moments is examined in detail. The method is easy to use, and provides a reliable a posteriori procedure to deal with the existence of strong radial couplings between adiabatic states, when a program to calculate the radial couplings exactly is not available.

Notes: When calculating the correlation energy where the effect of higher than double excitations is included by means of many-body Rayleigh-Schrödinger perturbation theory (MB-RSPT) through fourth order the problem of cancellation of exclusion-principle-violating (EPV) diagrams arises. The cancellation of EPV diagrams in fourth order of MB-RSPT is demonstrated for diagrams which include the effect of tetraexcitations.

Notes: Scope and limitations of different approaches which enable π electronic systems of topologically equivalent structures to be compared have been examined. Particular attention has been paid to analyses in terms of molecular subsystems.

Notes: A complete development of the PCILO method is presented for the INDO approximation. The introduction of exchange terms in the theoretical treatment is discussed and a detailed analysis of the successive contributions to the total energy is given. The method is applied to various conformational problems (geometry optimization, rotation, and inversion barriers). Its ability to deal with biological systems is tested on the acetylcholine neurotransmitter. Inversion barriers are highly improved with respect to the corresponding CNDO algorithm. A better account of σ-π exchange phenomena can be expected with the presented PCILO-INDO development.

Notes: In agreement with previous calculations by the authors, three definite resonances in the elastic electron-SF6 molecule scattering in the energy range 5-40 eV have been obtained with a multiple scattering method, elaborated originally for molecular bound states and modified here for scattering states. Results with various more-reliable one-electron potentials have been compared with previous calculations and available experimental data.

Notes: While regarding the elementary biological function as a series of elementary acts resulting in either chemical bond formation (breakage) or a changed molecular subsystem state, we would like to focus attention on some of the most essential and general features of this process in terms of the Von Neumann theory of self-reproducing automata.

Notes: The electron mechanism of the nonequilibrium vibration excitation is considered in multiatom molecules with the condition that the bottleneck effect takes place. The quantum-statistical theory states that if the simplest enzyme reaction is proposed on the basis of the vibrational energy recuperation idea, the vibrons emitted in producing the free product and enzyme activate the first stage of the formation of the Michaelis-Menten complex and the multiphonon feedback mechanism is realized. Resulting solutions are applied to explain some biochemical and genetic effects.

Notes: We suggest the explicit transformation of the parametrized atomic φ-basis semiempirical Hamiltonian to the Löwdin λ basis. A nontrivial problem then arises concerning the transformation of the four-index electron interaction matrix Γ, for which parametrization is given in the φ basis, whereas the NDO approximation is introduced in the λ basis. The main result is that under the CNDO assumption the two-index Coulomb matrix can be transformed independently of other integrals of Γ. The explicit form of the transformation between the Coulomb matrix γ of parameters given in the φ basis and the Coulomb matrix λγ in the λ basis is found. The λγ calculated by this method differs only slightly from the result of the exact complicated four-index transformation. On the other hand the elements of γ and λγ may differ by several eV when overlap is significant.

Notes: First- and second-order perturbation theory in a polarization approximation was employed to calculate interaction energies of planar xanthine-xanthine pairs in stable configurations. Electrostatic energy was obtained in the atomic-dipole approximation. The results provided a basis for formulation of a four-stranded model of poly(xanthylic acid) that allows two hydrogen bonds per base. The model accounts satisfactorily for the unusual thermal stability and the observed pH transition of the polymer. The latter is due to the gradual dissociation of the N3 protons accompanying by disrupture of the weak N3—H ··· O6 hydrogen bonds. However, the structure is only moderately weakened since the configuration of the coplanar bases remains stabilized by four N1—H ··· O2 hydrogen bonds.

Notes: Ab initio calculations within the minimal basis set of STO-4LGTO have been carried out on molecules of type H3MX (M = Si, C; X = H, NH2, OH, F). The influence of the MH3-group inversion on the electronic structure of these compounds has been investigated and illustrated by MO electron density maps. The ability of the central atom to form an additional bond has been estimated with the help of calculations on the complexes of these molecules with the hydrogen negative ion. The complexes of type [H4SiX]- have been found to be more stable than their unbonded components. The [H4CX]- complex formation has not proved to be advantageous.

Notes: The optical reflectivity spectra of quasi-one-dimensional polymers (SN)x, trans-(CH)x, and polydiacetylene are investigated in an energy range from 1 to 25 eV by use of synchrotron radiation. Observed structures associated with π-electron states are interpreted in terms of the quasi-one-dimensional one-electron bands calculated by the LCAO-type model.

Notes: The fractional parentage coefficients (CFPS) for arbitrary symmetry (including non-simply reducible point groups), different coupling schemes, and several open shells are discussed with emphasis on the common features. The differences between the coupling schemes arise merely from a different interpretation of the relevant symmetry group. The formulation uses the particle-number representation (so-called second quantization), in which the CFPS appear as the reduced matrix elements of the creation or annihilation operators. This shows, that there is no principal difference in the fractional parentage scheme of one or several open shells. For the latter case the theory of adjective CFPS is worked out and applied to an example of octahedral symmetry.

Notes: The concepts of “open assembly” is defined, and the hypervirial theorem is derived in three steps: (i) An equation of motion of the reduced density matrix of the first order is derived. (ii) This equation is utilized to derive a general equation of continuity for single-particle properties. (iii) The hypervirial equation for open assemblies is obtained as a long-time average of the continuity equation. The hypervirial theorem is shown to be equivalent to a simple postulate: no physical property can keep on accumulating for ever in a limited volume. Finally, the hypervirial theorem is applied to the problems of force, torque, and virial balance in open dynamical assemblies, and the results are compared with the corresponding classical results.

Notes: A large family of interlocking perturbational inequalities is derived by variational considerations for the stationary states of all systems described by a Hamiltonian linear in a real perturbing parameter λ. These inequalities constrain in many different ways the perturbation expansions of both exact and variational eigenvalues for these systems; analogous inequalities are derived for the components of the eigenvalues. A special feature of the analysis consists of obtaining inequalities applicable to the separate sums of even- and odd-order perturbation energies. For lowest states of each symmetry and for positive definite perturbing operator, the interlocking effect of the inequalities becomes extremely restrictive. The inequalities are illustrated with several numerical calculations for different systems and states of the helium isoelectronic sequence. The direction of the inequalities is found to be unaffected by low-order truncation, thus rendering them applicable to low-order perturbation expansions. The inequalities are used to study the efficacy of low-order perturbation theory for two- to ten-electron atomic isoelectronic sequences, and to determine the functional dependence upon λ of the eigenvalues and their components for arbitrary atomic isoelectronic sequences.

Notes: It is suggested that simple electronic shielding effects induced by wave function antisymmetrization tend to govern the energy ordering of singlet and triplet terms within a two-electron atomic configuration. This approach gives rise to the following alternating rule: For the term of greatest orbital angular momentum within a configuration, the triplet lies below the singlet. The energy ordering reverses for the term of next highest angular momentum, and continues to alternate with each change of one unit in the orbital angular momentum until the term of lowest angular momentum is reached. In an examination of over 600 energy levels of the elements and their ions, the alternating rule reliably orders singlet-triplet energy levels in some 90% of the cases.

Notes: A simple self consistent variation perturbation method in the coupled Hartree-Fock scheme has been proposed to calculate 1s2s 1S state of the He atom. The present paper deals with an 1s2s 1S wave function in which all the relevant orthogonality conditions are imposed in successive stages. The resulting wave functions together with some interesting features are discussed.

Notes: Paths of length two and three appear to dominate variations in isomers of alkanes when various physical and chemical molecular properties are compared. The regularities previously observed for octanes have been fully examined for the set of 35 nonane isomers C9H20. Such examinations are facilitated by construction of appropriate grid graphs with paths of length two and three, respectively, representing molecules and connecting such points along the grid axes. By ordering structures in the two-dimensional coordinate plane, various trends and regular changes in the relative magnitudes for the selected thermodynamic properties have been traced to molecular connectivity and topology.

Notes: We present a simple model for the calculation of some properties of disordered one-dimensional organic conductors. We focus our attention on two points: the decrease of the insulator-to-metal transition temperature and the increase of the highest electrical conductivity temperature that both occur when the amount of disorder is increased. We give an explanation that brings a new insight to the still little understood zone around the insulator-to-metal transition. The model enters the general framework of the alternant molecular orbital method and seems to be a priori restricted to systems such as NMP-TCNQ. We discuss its possible application to more complicated systems such as TTF-TCNQ.

Notes: It is shown that the Löwdin orthogonalization gives the unique minimum for the functional φ measuring the least squares distance between the given orbitals and the orthogonalized orbitals. Furthermore a much stronger result is obtained, namely that φ has only one local minimum, which is attained at the Löwdin orthogonalization and which is global. This justifies certain computer programs that compute Löwdin orthogonalization via minimization procedures. Finally there is a discussion of replacing the least squares metric by other metrics. The Löwdin orthogonalization turns out to be optimal with respect to all the commonly encountered norms.

Notes: In this paper an attempt is made to define charge transfer trying also other ways than Mulliken's population analysis. To illustrate this the amount of transferred charge (q) in the complexes HCONH2 + OHC - CHO in two relative geometrical positions, H2O + H2O and H2O + Li+ has been calculated with the help of Mulliken's population analysis using the wave function of the complex on the one hand and in the framework of different methods to subdivide the total space of the complex into subspaces for the acceptor and donor molecule, respectively, on the other hand. The results obtained show that Mulliken's population analysis gives a qualitatively correct description of the charge transfer process but to obtain the finer details most probably the use of a single number (q) is not sufficient. Further, the change in the total energy with respect to an effective charge transfer of a water dimer and of a solvent-cation complex has been investigated using the new mutually consistent field method. In this way the amount of transferred charge as well as the charge transfer interaction energy have been obtained in one step. These results have been compared with calculations applying second-order perturbation theory including overlap and the supermolecule method.

Notes: Average procedures of SCF methods are discussed. Although average operators are known from early Hartree-Fock times, some remarks against indiscriminate use of such operator forms may still be useful. In general, unless a very particular set of average structures is chosen, a dependence of final results on the SCF starting vectors is a troublesome fact. Consequently, energies, populations and molecular parameters in general may show unpredictable behavior under various trial vectors. It is shown that variationally coherent operator forms are given by state parameters with equal values for all the active MO's used in the construction of Coulomb and exchange terms throughout the SCF cycles.

Notes: A decomposition of an N-particle operator as a sum of N + 1 components is defined such that, in the case of a model system employing a finite one-particle basis set, the decomposition is invariant under unitary transformations of the basis set. Applied to a two-particle Hamiltonian, this decomposition gives rise to the distinction between the independent-particle energy and the coupling energy defined in previous papers. Applied to the reduced density operator for a quantum state, the decomposition corresponds to partitioning the density into irreducible components. This partitioning is illustrated by graphs of electron density for the water molecule.

Notes: The modified PCILO method, for which the use of the Rayleigh-Schrödinger many-body perturbation theory with the Møller-Plesset type of Hamiltonian partitioning is characteristic, has been extended to energy calculations of transition metal compounds. On the CNDO/2 level of the Hamiltonian approximation the energy and geometry of the ions CuX42-, MCl42- and the molecules CuX (X = F, Cl, Br; M = Mn, Fe, Co, Ni, Cu) have been calculated. The comparison with MO—LCAO—SCF calculations (CNDO/2-UHF) shows that the localized bonding model used here can be regarded as a good zeroth-order approximation describing the bonding situation in complexes of this type. The perturbation theory also provides an improvement of the harmonic force constants of the CuX molecules with respect to the SCF level of approximation.

Notes: A series of saturated XnHm (X being either C or Si) molecules is studied using the MINDO/3 and MNDO quantum-chemistry procedures. We find that the proximity of H atoms tends to shorten X—X bonds, and that this effect is (especially for MINDO/3) much larger than a similar trend in experimental values. The connection between this and hybridization values calculated from localized orbitals is investigated. It is found that the hybridization model works well for X—H bonds, whereas for X—X bonds non-σ-bond effects also play a significant role. It is shown that the changes in electronic structure may be directly connected to differences in X and H atomic levels, so that similar bond length differences may be expected in other molecular orbital calculations.

Notes: The quantum-mechanical methods (EHT and CNDO/2) have been applied to the homoallylic cation. Both methods successfully predict that the ion need not be represented as a nonclassical structure.

Notes: A nonlinear dynamical equation for the electronic collective motion is presented by employing the traditional time-dependent procedure. The equation is applied to the model π-electron system of ethylene, and the effects of nonlinear interactions are investigated using its several states as reference states. It is shown that the nonlinear correlation plays an important role in describing the change of the lower excited states.

Notes: Intensities of a1Δg←X 3∑g- and b 1∑g+ ← X 3∑g- transitions in molecular oxygen have been calculated on the basis of the INDO method taking into account spin-orbit coupling by perturbation theory. The transitions are magnetic dipole in nature. The first of them (a - X) steals its intensity from 3Πg-3∑g- and 1Πg-1Δg transitions, which are determined by the orbital angular-momentum operator. This source is not the principal one for the intensity of the second (b-X) transition. Its intensity is stolen principally from microwave transitions between spin sublevels of the ground 3∑g- state. The last source explains the large difference in intensities of the a-X and b-X transitions. Calculated oscillator strengths are in a good agreement with experiment. The same integrals that determine the intensity also determine the parameters of the spin Hamiltonian for the ground 3∑g- state. These parameters are in a good agreement with experiment also, showing the validity of the whole calculation. In a condensed phase the investigated transitions are enhanced by intermolecular exchange interaction. It is known that an external heavy atom (EHA) enhances the b-X transition of oxygen in solution, but does not influence the a-X transition. In the collision complex O2-EHA, which has a geometry without inversion symmetry, the microwave transitions between spin sublevels of the “3∑g-” state obtain electric-dipole moments, which are stolen from the charge-transfer transition. This mechanism explains the selective effect of EHA.

Notes: Potential-energy curves for CH4·CH4 have been calculated using the SCF LCAO MO method. Six different mutual orientations of the molecules have been considered and several basis sets have been employed. An analytical potential has been fitted to the computed energy values and used in a Monte Carlo calculation to yield a spherically averaged CH4·CH4 potential. The potential, if corrected for dispersion interaction, agrees fairly well with that derived from thermophysical data. At short distances it disagrees with the potentials derived from scattering experiments which, however, are also incompatible with the experimental potential for large distances.

Notes: A scheme is presented for performing linear-combination-of-atomic-orbitals (LCAO) self-consistent-field (SCF) ab initio Hartree-Fock calculations of the electronic structure of periodic systems. The main aspects which characterize the present method are (i) a thorough discussion of both translational and local symmetry properties and the derivation of general formulas for the transformation of all the relevant monoelectronic and bielectronic terms under symmetry operators. (ii) The use of general yet powerful criteria for the truncation of infinite sums; in particular, the Coulomb electron-electron interactions are subdivided into terms corresponding to intersecting or nonintersecting charge distributions; the latter are grouped into shell contributions and the interaction is evaluated by multipolar expansions; the exchange interaction may be evaluated with great precision by retaining a relatively small number of two-electron integrals according to a truncation criterion which fully preserves its nonlocal character. (iii) The use of a procedure for performing integrals over k, as needed in the evaluation of the Fermi energy and in the reconstruction of the Fock matrix, which is particularly simple because it employs partially intersecting small spheres as integration subdomains where linear extrapolation is admitted. A comparison is finally made of our fundamental equations in the critical SCF stage with those obtainable by a recent proposal which uses Fourier transforms to express Coulomb and exchange integrals.

Notes: The ab-initio LCAO-HF method that was presented in a previous work is applied here to the study of graphite and hexagonal boron nitride monolayers. The dependence of total energy, band structure and density matrix on the computational parameters that control truncations in infinite sums over the translation vectors g of the direct lattice is first considered. For these systems it comes out that very good results can be obtained by neglecting all but the first few terms in the sums. For instance, for exchange contributions it is sufficient to consider integrals associated with the first 13 g vectors, suitably grouped, to obtain an error in total energy below 0.0001 a.u. The calculations were performed using an STO-3G basis set; results concerning conformational minimum, bond energy, symmetric force constant, band structure, density of states, and population analysis are presented and discussed.

Notes: This paper investigates the polarization effects associated with functional processes in photosynthetic membranes.

Notes: A modified form of Frenkel's time-dependent variation principle, suggested by McLachlan for state vectors, is employed to discuss the optimal time evolution of a density operator ρ(t). An ansatz is made for this operator such that i(dρ/dt) = [S, ρ], where S(t) is a linear combination of operators belonging to a particular manifold of “basis operators.” The expansion coefficients are required to minimize the error Tr{[S - H, ρ]† [S - H, ρ]}. Linear response functions corresponding to the variationally determined density operator are compared to those derived by means of linear decoupling procedures for propagators based on the same operator manifold. The two approximation schemes are not equivalent, in general, and several consistency requirements must be fulfilled before it can be ascertained that a given linear decoupling procedure corresponds to an optimal time development of the density operator in the sense of McLachlan. Finally, the general applicability of the suggested variation principle is discussed.

Notes: The Gaussian lobe representation of 2p and 3dxy functions of a one-electron atom has been reconsidered. Contrary to earlier results, it has been found that the minimum energy associated with the simplest case of these functions is reached when the expansion centers coincide with the nucleus. This also seems to be true for representations with larger expansion lengths. Under similar conditions, Whitten's octahedral representation of the 2p function gives a better energy value than Poshusta's tetrahedral one.

Notes: The second-order dispersion energy between interacting hydrogen pairs has been evaluated by the Borel-integral method. The results are in complete harmony with those obtained by the method of Padé approximants.

Notes: This paper gives an abbreviated method for the calculation of the density of states of a crystal on the basis of that band theory in which the crystal electron states are represented by the standinglike wave functions classified according to the point-group symmetry species. The crystal is a large but finite sphere filled regularly with atoms, and the wave functions are quantized at the boundary of the sphere. The Bloch theorem is not satisfied in this theory since the wave functions are not basis functions of the irreducible representations of the translation subgroup. On the other hand, a theorem is established that the density of states can be made up of contributions given by all irreducible representations of the crystal point group, any contribution being proportional to the square of the dimension of the irreducible representation. In distinction to a former approach, the band structure is calculated solely from the energy eigenvalues obtained with the aid of the diagonalization process of the Wannier-Slater differential operator. A simple cubic lattice with an s atomic orbital on each lattice site is taken as an example, and the results are compared with Bloch's theory.

Notes: The Van der Waals molecules Ar · HF, Ar · H2O, and Ar · HCl have been analyzed with potential surfaces obtained by SCF energies corrected for the basis set superposition error and by including dispersion forces. The computed properties for these Van der Waals molecules are in good agreement with recent experimental observations.

Notes: The many-body Green's function method is applied to the vertical ionization potential of the hydrogen molecule. The ionization potential is calculated iteratively by expanding the self-energy part up to third order. The effects of higher-order correlation corrections and nondiagonal self-energy elements on the solutions of the Dyson equation are examined with some techniques and approximations, by means of which a Koopmans' defect of 97.7% of the accurate value is obtained.

Notes: The total dipole moments, molecular energies, and π-electron densities for the linear and orthogonal pyrrole⃛acetonitrile hydrogen-bonded complexes were studied in the ab initio valence bond framework using the minimal STO-3G basis set. That the orthogonal conformation, although slightly less stable than the other, is predominant as observed in carbon tetrachloride, can be explained by its relatively high symmetry number.

Notes: The Hückel-London theory has been applied to the calculation of the “ring currents” octopole hypersusceptibilities of a series of conjugated compounds. Our calculations have been performed using fourth-order Rayleigh-Schrödinger perturbation technique. This is believed to be the first calculation of this kind. It is found that the values of “ring currents” hypersusceptibilities of fulvene and azulene are larger, in absolute magnitude, than the values corresponding, respectively, to benzene and naphthalene. It is found that, in most cases, the “ring currents” hypersusceptibilities are diamagnetic (negative values) for aromatic molecules and paramagnetic (positive values) for pseudoaromatic or antiaromatic compounds.

Notes: The SCF potential surface of the ground state for NO2 was calculated by using program JAMOL 3. The McLean-Loew-Berkowitz CGTO's were used as basis functions. One of the two N—O distance R is fixed to 2.25 a.u. and the other one r and the ONO angle θ are varied from 2.25 to 5.0 a.u. and from 0° to 180°, respectively. The potential surface has the minimum around r = 2.50 a.u. and θ = 120°, where the energy is found to be -203.954 a.u.

Notes: Within the framework of the LCAO-MO theory, a novel sign-alternation rule has been found empirically for the lowest excited ππ* triplet state in the alternant aromatic system. This rule can be applied to identify the phosphorescent state.

Notes: Various criteria that have been suggested for assessing the accuracy of complex-coordinate eigenvalues are critically tested in an application to the lowest helium 1S resonance, and found to be relatively ineffective. An alternative criterion is described, based on a generalized stabilization procedure, which seems better able to select the “best” resonance eigenvalue and to guide the construction of variational trial functions.

Notes: A new approach to evaluate the determinant of the adjacency matrix is presented in this paper.

Notes: Graph- and information-theoretical indices were recently developed as quantitative structural characteristics of molecules. In this paper they are found to correlate well with a number of molecular properties of alkylbenzenes: heats of formation, combustion (both in liquid and gas phase) and vaporization, molecular volume, boiling point, and parachor. The topological information index and the number of carbon atoms are taken as variables. The correlation coefficient was found to be equal or close to 1. In three cases the mean relative error is less than 0.1%, in another three cases it is within the range 0.2-0.4%, and for boiling points only it is 1.25%. The proposed approach is compared with the additive scheme of Tatevskii.

Notes: A new parameterization for the first transition metal has been proposed in the framework of CNDO/2 method. We carried out CNDO/2 calculation of hexamine complexes [M(NH3)6]2+ and hexa-aquo complexes [M(OH2)6]2+ in the high spin state where M = Mn, Fe, Co, Ni, and Cu, using new parameters. It is shown that the calculated order of binding energy is Mn—L 〈 Fe—L 〈 Co—L 〈 Ni—L ≈ Cu—L (where L means the ligand), and is in good agreement with experiment. We discussed how the orbital nodes affect the nature of bonding between metal and ligand.

Notes: Molecules exposing considerable microsurface areas to the surrounding solvent such as amino acids, nucleotide bases in biopolymers, or various drug molecules, antigens, and substrates, tend to be pulled apart or pushed together as the case may be by the surrounding solvent medium. These solvophobic forces and their quantitative theory were introduced sometime earlier [O. Sinanoğlu, in Molecular Associations in Biology, B. Pullman, Ed. (Academic, New York, 1968), pp. 427-445; and references therein]. The forces involve both enthalpy and entropy effects. The case in water had been shown to involve particularly strong forces but not differing in kind from other solvents. There are still somewhat contradictory views on the aqueous case, referred to in the literature as “hydrophobic bonding” treated as a phenomena unique to water and previously thought to involve only entropic effects. The temperature dependence and volumetric effects on the earlier type of “hydrophobic bonding” are presently not always reconcilable with recent experimental evidence. By contrast, the solvophobic force theory allows the calculation of the full solvent effect on various association or isomerization equilibria using its quite rigorous relations and basic data derived with it from liquids and solutions. [cf., e.g., for an early application to cis-trans azobenzene isomerization, T. Halčǐoǧlu and O. Sinanoğlu, Ann. N.Y. Acad. Sci., 158, 308 (1969)]. The solvophobic force theory had also introduced as a measurable new quantity, “the thermodynamic microsurface area change of a reaction,” which is now finding considerable use in protein chemistry [cf., e.g., F.M. Richards and T. Richmond, in CIBA Symposium Proceedings on Molecular Interaction and Activity in Proteins (CIBA, New York, 1977)]. Solvophobic force theory has been tested and applied recently in detail in high pressure liquid chromatography (HPLC) by C. Horvàth, W. Melander, and I. Molnar [J. Chromatograph. 125, 123 (1976)] who verified the predicted temperature, molecular surface area, and salt concentration dependence. It worked well when applied in detail to the complicated methanol-water mixtures as well. The theory also gave the first a priori derivation of the experimentally well-known protein salting-in-salting-out curve [W. Melander and C. Horvath, Arch. Biochem. Biophys. 183, 200 (1977)]. We have now extended the theory further with new basic derivations which eliminate the need for the direct calculation of some cumbersome effects. The theory has also been recently applied to a number of new areas including drug-receptor interactions, aqueous amino acid interactions, and to multicomponent phase equilibria; the latter also of chemical engineering interest. Solvophobic interactions, although part statistical thermodynamical in nature, were shown to be usable as if they were an ordinary U(R) potential added on to quantum-chemical intrinsic in vacuo potentials for prediction of conformations in solution [O. Sinanoğlu, in The World of Quantum Chemistry, R. Daudel and B. Pullman, Eds. (Reidel, Dordrecht, 1974)]. There have also been some recent applications that illustrate the convenience of our solvophobic theory in correcting for solvent effects once quantum-mechanical molecular electronic structures and potential-energy surfaces are computed.

Notes: MINDO/3 calculations have been performed on the Clostridium MP flavodoxin active site (a complex of the redox active coenzyme flavin mononucleotide sandwiched between the side chains of methionine and tryptophan) at various redox levels using coordinates derived from x-ray diffraction studies of the holoenzyme. Frontier orbital indices were calculated and indicate that reduction of the flavin is accompanied by induced polar states in the amino acid side chains. This stabilization of charge by the amino acid side chains could account for the reaction rate enhancement of flavin reduction catalyzed by flavodoxin. Frontier orbitals for free flavin, for the flavodoxin bound flavin without the amino acid side chains, and for the oxidized Desulfovibrio vulgaris flavodoxin active site were computed for comparison.

Notes: The electronic structures of catechol derivatives, 3,4-dihydroxy-1-substituted benzenes, including epinephrine and norepinephrine, were calculated by means of the CNDO/2 and the MINDO/3 methods. Correlation between the maximum velocities divided by the molecular weight, as between the inverse of Michaelis-Menten constants in the O-methylation reaction catalyzed by catechol-O-methyltransferase and the electronic indices calculated on the basis of the frontier electron theory was found. The correlation coefficient between the observed maximum velocities divided by the molecular weight and the calculated ones was 0.873. The regression analysis showed that the Coulombic forces at the C3 and C4 positions and the electron acceptable indices at C6 and meta-O positions represented the best correlation with the biological activities (Vmax and Km). The electronic indices of the catechol moieties represent the rate-limiting factor of the O-methylation reaction.

Notes: Ligand-field theory is treated in a systematic and unified way by means of Lie algebra.

Notes: Binding energies of ionized donor-exciton complexes in crystals of CdSe, CdTe, and ZnSe are calculated using the most realistic effective potentials available for the electron-hole interaction.

Notes: The analysis of nonadditive effects in small palladium clusters via LCAO-MO-SCF calculations using the nonempirical pseudopotential model is presented. The results are tentatively correlated with previous studies on various metal clusters (Li, Be, Mg, etc.) for which a good knowledge of multibody terms has provided a valuable guide for understanding the cluster stabilities and their chemisorption capacity.

Notes: The emission spectra and lifetimes of the vapor-phase exciplexes of four cyano-substituted anthracenes with N,N-dimethylaniline (DMA) as a donor are examined over a wide temperature range. The activation energies associated with the exciplex dissociation are calculated to be of the order of 10 kcal/mol. The entropy change in forming the exciplexes is discussed in relation to the efficiency of the exciplex formation. For various donors other than DMA, preliminary results on how they interact with excited 9,10-dicyanoanthracene are also given.

Notes: Quantum-mechanical calculation of spectral intensity is done for the transitions from a particular vibrational level of the excited state E 1∏u to the discrete vibrational levels and dissociative continuum of the ground state X1Σg+ of the Cs2 molecule. The results are compared with the observed spectra by referring to the conservation of nuclear kinetic energy during the electronic transition.

Notes: Emission spectra and decay times of the fluorescence under the excitation of various energies were measured in pyrene crystals. At liquid nitrogen temperature, a new excimer emission was found under 390 nm excitation, and its peak shifts a little to the high energy in comparison with that of the familiar excimer. The decay time of the former emission abruptly changes around 125°K, which seems to be due to the phase transition in pyrene crystals. Also, when the crystals were rapidly cooled below 125°K, the monomer emission in the crystals was observed, and its decay time was about 600 nsec.

Notes: A new algorithm for calculating characteristic coefficients is proposed.

Notes: Relativistically parametrized extended-Hückel (REX) calculations are reported for MX4 (M = Ti, Zr, Hf, C, Si, Ge, Sn, Pb; X = Cl, Br, I) and for M(CH3)4 (M = Ti, C, Si, Ge, Sn, Pb). Satisfactory agreement is obtained with experiment and with earlier assignments both for the energy levels and for their relativistic splittings. This encourages the use of REX for assigning PES spectra. Double-ζ radial functions (REX and EHT) are given for Cl, Br, and I.

Notes: This investigation is a continuation of a study on the optimality of MO basis sets of Gaussian functions, when constructed from AO basis sets optimized for the neutral atom or for ions. A formal charge parameter Q is used to adjust AO basis sets to the molecular environment, by virtue of a simple quadratic equation. Calculations are performed on a series of seven C2 hydrocarbons (C2H2, C2H4, C2H6, C2H3+ (open), C2H3+ (bridged), C2H5+ (bridged), and C2H4- radical anion). A simple rule is formulated to give approximate values of the charge parameter Q.

Notes: Variational iterative solutions for multipole polarizabilities of the H atom have been carried out. The resulting numerical values of the Cauchy coefficients are in harmony with our recent work. The large frequency expansion of the multipole polarizabilities of the H atom is also calculated. The first term in such expansions, the multipole oscillator strength sum rule, is in harmony with earlier work.