Kenneth J. Miller

A Theoretical Model for the Binding of Cis-Pt(NH3)2 +2 to DNA

The binding of cis-Pt(NH3)2B1B2 to the bases B1 and B2, i.e., guanine (G), cytosine (C), adenine (A), and thymine (T), of DNA is studied theoretically. The components of the binding are analyzed and a model structure is proposed for the intrastrand binding to the dB1pdB2 sequence of a kinked double helical DNA. Quantum mechanical calculations of the ligand binding energy indicates that cis-Pt(NH3)2(+2) (cis-PDA) binds to N7(G), N3(C), O2(C), O6(G), N3(A), N7(A), O4(T) and O2(T) in order of decreasing binding energy. Conformational analysis provides structures of kinked DNA in which adjacent bases chelate to cis-PDA. Only bending toward the major groove allows the construction of acceptable square planar complexes. Examples are presented for kinks of -70 degrees and -40 degrees at the receptor site to orient the base pairs for ligand binding to B1 and B2 to form a nearly square planar complex. The energies for complex formation of cis-PDA to the various intra-strand base sites in double stranded DNA are estimated. At least 32 kcal/mole separates the energetically favorable dGpdG.cis-PDA chelate from the dCpdG.cis-PDA chelate. All other possible chelate structures are much higher in energy which correlates with their lack of observation in competition with the preferred dGpdG chelate. The second most favorable ligand energy occurs with N3(C). A novel binding site involving dC(N3)pdG(N7) is examined. Denaturation can result in an anti----syn rotation of C about its glycosidic bond to place N3(C) in the major groove for intrastrand binding in duplex DNA. This novel intrastrand dCpdG complex and the most favored dGpdG structure are illustrated with stereographic projections.

Dependence of Generalized Oscillator Strengths of Ethylene on Momentum Transfer

Generalized oscillator strengths are calculated as a function of scattering angle or K, the momentum transfer, for seven electronic transitions in ethylene in order to characterize each type of transition. The valence transitions 1Ag → 1B1u[π → π*] and 1Ag → 1B1g[σ → π*], and the Rydberg transitions 1Ag → 1B1g[π → σ*], 1Ag → 1B2g[π → σ*], 1Ag → 1B3u[π → σ*], 1Ag → 1B3g[σ → σ*] and 1Ag → 1B3u[π → σ*] are studied. Characteristic minima in f(K) for the Rydberg transitions appear. This behavior is attributed to the presence or absence of nodes in the molecular orbitals. It is suggested that this phenomenon be used as a probe of the type of molecular orbitals which are involved in a particular transition as well as the location of optically forbidden transitions. Qualitative agreement is obtained with experimental results for all but the π → π* transition, which does display a minimum. This is probably due to configurational mixing with Hartree–Fock Rydberg states.

Energy levels and potential energy curves for H2, N2, and O2 with an independent particle model

Energy levels for valence and Rydberg states are calculated for H2, N2, and O2. An independent particle model (IPM) with an effective one‐electron potential whose nuclear charge depends on the electron position is utilized to approximate the Coulomb and exchange interactions. An analytical generalization of the potential parameters to reflect a change in internuclear separation yields accurate average molecular potential energy curves E(R) when experimental ion energies E+(R) are added to IPM molecular orbital energies e(R), viz., E(R)=E+(R)+e(R). A convergence formula for incrementing the energy in the numerical integration procedure is presented.

Dependence of extrema in the generalized oscillator strengths on momentum transfer and effective nuclear charge for atomic transitions

Generalized oscillator strengths f(K) for one‐electron atomic transitions involving atoms in the first through third rows of the Periodic Table are studied within the first Born approximation. A one‐electron model employing hydrogenlike orbitals is used with appropriate effective nuclear charges. For single electron excitations, the Born matrix element f(K) = 2Δ E|∫ φb*e iK· rφadV|2/K2 can be scaled to yield a reduced generalized oscillator strength f (κ) which depends on the ratio of effective nuclear charges ζ(final)/ζ(initial), and a reduced momentum transfer κ = K /ζ(initial). Transitions to a Rydberg series exhibit extrema in f(K) which are nearly the same for all members of the series, whereas excitations to different series exhibit a different number and positioning of the extrema. This behavior suggests that trends in generalized oscillator strengths can be used as an experimental tool to probe various types of transitions and to unravel Rydberg series. Comparison of theoretical calculations with ...

Hydrogen bonding in Pt ammine complexes

Abstract Hydrogen bonding stabilizes the binding of Pt ammine cations to oligonucleotides. Model calculations explore the energetics of the binding of the ammine to G (O6) in PtA 3 G (A = ammine, G = guanine) and the intermolecular binding of a carbonyl oxygen to the aremine in a complex of PtA 4 and formaldehyde as a model of binding to carbonyl sites in thymine. Hydrogen-bondig interaction to the G(O6) site is weak but permits the close approach of the O6 and H atoms. Intermolecular hydrogen bonding is strong, as expected for an optimal ionic hydrogen bond.

Generalized oscillator strengths and total cross sections for H2, N2, and O2 with an independent particle model

Generalized oscillator strengths, oscillator strengths, and total cross sections are calculated within the first Born approximation for 1σg→nσu and nπu transitions in H2; for selected 2σu, 1πu, and 3σg to nπg, nπu, nσg, nσu, and nδg transitions in N2; and for the 1πg→nπu excitations in O2 in addition to transitions equivalent to those studied in N2. When compared with the corresponding experimental spin‐allowed excitations good agreement is obtained in most cases. The spheroidal potential approximation within the independent particle model (IPM) is analyzed as the source of the problem for several of the transitions in N2 and O2 which yield properties smaller than the experimental results by 2 orders of magnitude. The theoretical result, previously unreported, for the 1πu→1δg transition in N2 suggests that its intensity should be compared to the 1πu→1πg(b′←X) and that it corresponds to the e←X transition. The theoretical result for the 1πu→1δg transition in O2 for which there is no experimental data is al...

Linear dependency in the refinement of force constants with the Jacobian method

The Jacobian method in the refinement of force constants is studied. Theoretical and experimental frequencies and other observables, νs, are matched by minimizing ΣsWs(ν  sexp – ν  sth )2, where s = 1, 2, 3,…, proceeds over all normal modes and isotopes, and Ws are weighting factors. Modification of the theoretical frequencies is accomplished with the Jacobian matrix, J, with elements Jsi = ∂νs/∂ki involving each force constant or associated parameter, ki, i = 1, 2, 3,…, by Δν = JΔk. The parameters are adjusted directly with Δk = (JTWJ)−1(JW) Δν, where W is a diagonal matrix which weights the frequencies. The linear dependence problem must be addressed prior to inversion of JTWJ. The approach entails diagonalization of JT WJ, analysis of the components of the eigenvectors associated with zero and small eigenvalues, identification of the linearly dependent parameters, successive elimination of selective parameters, and a repeat of this procedure until linear dependency is removed. The Jacobian matrices are obtained by differencing the frequencies when the parameters are varied and by numerical and analytical evaluation of the derivative of the potential. The unitary transformation, U, used to calculate J = UT (∂F/∂k)U or J = UT (ΔF/Δk)U, is obtained from the diagonalization of the Hessian, Fmn = ∂2ν/∂pm∂qn, where p, q = x, y, z are the Cartesian coordinates for atoms m, n = 1, 2, 3,…, at the initial value of ki, i = 1, 2, 3, ⃜ The accuracy of and the ability to evaluate the Jacobian matrix by these methods are discussed. Applications to CH4, H2CO, C2H4, and C2H6 are presented. Linearly dependent and ill‐conditioned parameters are identified and removed. The procedure is general for any observable quantity.

An empirical rule relating fundamental to harmonic frequencies

An empirical approach to estimate harmonic frequencies from experimental fundamental vibrational frequencies is presented. It is based on a partitioning of the eigenvectors of each normal mode, s = 1, 2, 3,…, 3N − 6, into internal motion components involving bond stretching, Bs, angle bending, As, torsional motion, Ts, and out-of-plane motion, Os. This is called the BATO method. An empirical function, fs = (1250Bs + 2000As + 1300Ts + 1600Os) A, is developed to assign relative anharmonic contributions to each kind of internal motion by relating harmonic frequencies, ωs, to the anharmonic or fundamental frequencies, νs, with νs = ωs + 2χs = ωs(1 − fsωs). The anharmonic states are assumed to satisfy a Morse expression, νsn = ωs(ns + 12) + χs(ns + 12)2, where ns = 0, 1, 2, ⋯ denote the vibrational states of mode s. The coefficients of fs are calibrated with the available experimental data for νsexp and ωsexp with isotopes of 19 molecules which contain bonds and groups required for biochemical applications. The objective is to use the BATO method to estimate empirical harmonic frequencies, ωsemp, from experimental fundamental frequencies, νsexp, in a self-consistent procedure in cases where ωsemp are not known. Of the 394 states in 19 molecules studied, the method yields results within 10 cm−1 for 232 states. 11–20 cm−1 for 86 states, 21–30 cm−1 for 45 states, 31–40 cm−1 for 19 states, 41–60 cm−1 for 9 states, and 61–81 cm−1 for 3 states tested. Detailed results are presented for the molecule containing the most common isotope. The maximum errors occur in C2H6 and C3H8, for which the method tends to overestimate the CH stretch in several cases where the comparison is against Dennisons rule. All molecules studied satisfy the product and summation rules well.

Statistical Error in Molecular Cross Section Measurements

The probability that a set of counts of particles transmitted over a measured path through a gas at a sequence of pressures can correspond to a particular value of the total cross section is calculated. From this, recipes are given for determining the best value of the cross section and of its mean square deviation, for evaluating the random and systematic errors in the cross section caused by random fluctuations in gas pressure and errors in the reading of gas pressure, and for prescribing the parameters of an experiment to achieve maximum precision in a given time of measurement.

Evaluation of atomic scattering integrals by numerical techniques

Abstract Integrals needed in calculations of electron scattering off atoms are solved. The basis functions consist of Slater-type functions to describe the bound-like character of the wavefunction, and spherical Bessel functions of the first and second kind for the free particle portion. A damping factor is used with the latter Bessel function to insure proper behavior at the origin. With integral representations of the Bessel functions, numerical techniques are developed to obtain all one- and two-electron integrals.