FH Molecules Research Articles

Elucidation of the Electronic Structure of Molecules with the Help of NMR Spin−Spin Coupling Constants: The FH Molecule

It is demonstrated how the one-bond NMR spin-spin coupling constant (SSCC) (1)J(FH) can be used as a source of information on the electronic structure of the FH molecule. For this purpose, the best possible agreement between measured and calculated SSCC is achieved by large basis set coupled perturbed density functional theory calculations. Then, the calculated value is dissected into its four Ramsey terms: Fermi contact, the paramagnetic spin-orbit term, the diamagnetic spin-orbit term, and the spin dipole term, which in turn are decomposed into orbital contributions and then described by their spin densities and orbital current densities. In this way, the SSCC gives detailed information about the electronegativity of F, the bond polarity, the bond polarizability, the volume and the polarizability of sigma and pi lone pair orbitals, the s- or p-character of the bond orbital, the nature of the LUMO, and the density distribution around F.

Comparison of the polarizabilities and hyperpolarizabilities obtained from finite basis set and finite difference Hartree–Fock calculations for diatomic molecules: II. Refinement of basis sets and grids for hyperpolarizability calculations

In a previous paper, we have made a comparison of the accuracy with which the electric dipole polarizability αzz and hyperpolarizability βzzz can be calculated by using either the finite basis set approach (the algebraic approximation) or the finite difference method in calculations for the ground states of the H2, LiH, BH and FH molecules, at their respective experimental equilibrium geometries, within the Hartree–Fock model. A re-examination of the hyperpolarizability of the BH molecule shows it to be very sensitive both to the choice of grid employed in the finite difference Hartree–Fock calculation and the construction of the basis set used in the matrix Hartree–Fock study. A new comparison of finite difference and finite basis set hyperpolarizabilities for the BH molecule is made, together with new calculations for the LiH and FH ground states.

C–H⋯X interactions of fluoroform with ammonia, water, hydrogen cyanide, and hydrogen fluoride: conventional and improper hydrogen bonds

The structural changes, dipole moments, and interaction energies for a series of C–H⋯X hydrogen bonded complexes involving F3CH as proton donor and NH3, OH2, NCH, and FH as proton acceptors have been studied using ab initio calculations including electron correlation effect for various basis sets. The NH3 shows a conventional hydrogen bond, while the other molecules show improper hydrogen bonds as evidenced by the C–H bond length shortening and the blue-shift of C–H stretching vibrational frequency. In the complex of F3CH⋯NCH, both C–H and N–C bonds are contracted, and their corresponding stretching vibrational frequencies are blue-shifted compared with monomers. The blue-shifted stretching vibration in the proton acceptor molecule has not been much addressed until now. Both conventional and improper hydrogen bonds are noted in the nonlinear complex of F3CH⋯FH, where FH molecule plays a dual role of proton acceptor and donor at the same time. The interaction energies are almost equivalent for HF and MP2 calculations, which does not support a recent proposition that the dispersive interaction is the origin of improper H-bonding.

The human complement regulator factor H binds pneumococcal surface protein PspC via short consensus repeats 13 to 15.

The innate ability of Streptococcus pneumoniae to resist complement activation and complement-mediated phagocytosis may be a direct consequence of the ability of the bacteria to bind components of the complement regulatory system. One such component, factor H (fH), is a crucial fluid-phase negative regulator of the alternative pathway of complement and is utilized by a number of pathogenic organisms to resist complement attack. The pneumococcal surface protein C (PspC [also known as CbpA] and SpsA) has been shown to bind fH, although the exact binding site within one or more of the 20 short consensus repeats (SCRs) of the molecule is not known. The purpose of the current study was to map specific SCRs on fH responsible for this binding. Initial experiments utilizing type 2 pneumococcal strain D39 and its isogenic PspC-negative derivative (D39/pspC mutant) showed that fH binding was PspC dependent. A purified recombinant protein derivative of PspC that lacked the proline-rich region (PspCDeltaPro) had a reduced binding efficiency for fH, thereby directly showing the importance of this region for the fH interaction. We have specifically shown by inhibition experiments that SCRs responsible for heparin and C3b binding of fH are not involved in binding PspC and the interaction between fH and PspC is largely hydrophobic, since no inhibition was observed in the presence of high concentrations of NaCl. Construction of SCR proteins encompassing the whole fH molecule showed that SCRs 8 to 15 (SCR 8-15) mediated binding to PspC. Further localization experiments revealed that SCR 13 and SCR 15 were required for full binding, although partial binding was retained when either SCR was removed.

Three-dimensional quantum time-dependent study of the photodissociation dynamics of Na⋯FH/D

A time-dependent three-dimensional nonadiabatic computation study of the photodissociation of the van der Waals Na ⋯ FH molecule was performed for total J=0. A very low probability of photo-reaction to produce NaF + H was observed from most initial conditions. Enhancement of the NaF + H product was observed for the isotopically substituted Na ⋯ FD. The three-dimensional calculations are in qualitative agreement with the two-dimensional previous study. Calculated excited state lifetimes were in the range of ∼100 ps. Excitation of the bend and the van-der Waals stretch significantly shortened these lifetimes without increasing the reaction yield.

The Fourier method for tri-atomic systems in the search for the optimal coordinate system

The Fourier grid method has been implemented on four tri-atomic coordinate systems. The explicit forms of the kinetic-energy operators are presented and the method of implementation described. The coordinates tested are the perimetric, Eckart, Jacobi, and conformal Euclidean. A comparative study was carried out using propagation techniques to obtain the lowest vibrational eigenvalues on the H3+ and the van der Waals Na⋅⋅⋅FH molecules for J=0. Converged eigenvalues were obtained for all the coordinate systems tested. The wavepacket representation methods were also compared for the nonadiabatic photodissociation dynamics of the Na⋅⋅⋅FH. When the coordinate systems matched the topology of the potential-energy surface, significant reduction in the grid size was obtained. The analysis has led to a method for evaluating grid efficiency and optimization based on a classical phase space approach.

Comparison of thepolarizabilities and hyperpolarizabilities obtained from finitebasis set and finite difference Hartree-Fock calculations fordiatomic molecules

A comparison is made of the accuracy by which the electricdipole polarizability αzz andhyperpolarizability βzzz can be calculated byusing the finite basis set approach (the algebraicapproximation) and finite difference method in calculationsemploying the Hartree-Fock model. The numerical and algebraicmethods were tested on the ground states of H2, LiH, BH andFH molecules at their respective experimental equilibriumgeometries. For the FH molecule at its experimentalequilibrium geometry, a sequence of distributed universaleven-tempered basis sets have been used to explore theconvergence pattern of the total energy, dipole moment andpolarizabilities. The comparison of finite difference and finitebasis set methods is extended to geometries for which thenuclear separation, RFH, lies in the range1.5-2.2 b. The methods give consistent results to within 1%or better. In the case of the FH molecule the dependenceof truncation errors of the total energy, dipole moment andpolarizabilities on the geometry have been studied and are shownto be negligible.

Bound and quasibound states of the Na⋯FH van der Waals molecule

A recently developed diabatic representation for the two lowest A'2 electronic states of the NaFH system [M.S. Topaler, D.G. Truhlar, X.Y. Chang, P. Piecuch, and J.C. Polanyi, J. Chem. Phys. 108, 5349 (1998)], augmented with highly accurate multireference configuration interaction data, is used to construct a new potential energy function for the ground electronic state of NaFH. The refined potential is used to calculate the bound and quasibound rovibrational states of the Na⋯FH molecule. The focus is on the quasibound states corresponding to excitation of the H–F mode in the complex, although states in which the H–F mode is not excited are also studied. All rovibrational calculations are performed within the framework of the Sutcliffe–Tennyson Hamiltonian for triatomic molecules. The energy positions and lifetimes of quasibound states are obtained using the stabilization method. Three methods are employed to solve the rovibrational problem: (i) the variational approach, in which the Hamiltonian matrix, as defined by a discrete basis set, is diagonalized, (ii) the coupled-channel method, in which the van der Waals stretching coordinate is handled by direct numerical propagation on a grid, and (iii) two perturbative approaches based on the adiabatic separation of vibrational motions. The effect of rotational excitation on the lifetimes of calculated resonances is studied. The main results of this study are the strong evidence for the existence of many long-lived rovibrational resonances corresponding to excitation of the H–F mode in the complex and the rationalization of this finding in terms of effective potentials defining adiabatic separations. Possible impact of the results obtained in this study on new experimental ways of probing potential energy surfaces of the NaFH system, with emphasis on the dynamics of photo-induced charge transfer in Na⋯FH, is discussed.

Calculation of frequency-dependent second hyperpolarizabilities for electric field induced second harmonic generation in the second-order Mo/ller–Plesset perturbation theory

The calculations of frequency-dependent second hyperpolarizabilities for the (static) electric field induced second harmonic generation (ESHG) [γ(−2ω;ω,ω,0)] of the FH, H2O, CO, and NH3 molecules in the second-order Mo/ller–Plesset perturbation theory (MP2) based on the quasienergy derivative (QED) method are performed by numerical differentiation of frequency-dependent first hyperpolarizabilities for the second harmonic generation (SHG) [β(−2ω;ω,ω)] with respect to static electric fields. The QED-MP2 values of the ESHG second hyperpolarizabilities γ∥(−2ω;ω,ω,0) of the H2O, CO, and NH3 molecules show good agreement with the experimental values.

Calculation of frequency-dependent first hyperpolarizabilities using the second-order Møller–Plesset perturbation theory

We perform the first calculations of frequency-dependent first hyperpolarizabilities in the second-order Møller–Plesset perturbation theory (MP2) as analytical third derivatives of the time-averaged MP2 quasienergy with respect to electric field strengths. The calculations of frequency-dependent first hyperpolarizabilities using the quasienergy derivative (QED) method-based MP2 (QED-MP2) response theory are presented for the electro-optic Pockels effect (EOPE) [β(−ω;ω,0)] and second harmonic generation (SHG) [β(−2ω;ω,ω)] of the FH, H2O, CO, and NH3 molecules. The QED-MP2 values of the SHG first hyperpolarizabilities β∥(−2ω;ω,ω) for the H2O, CO, and NH3 molecules show good agreement with the experimental values. The QED-MP2 response theory is the simplest in ab initio methods for including dynamical electron correlation effects in dynamic response properties efficiently.

CSF-based multireference coupled-pair approximation. IV. Revision of coupling term and application to Rydberg-valence avoided crossing in lowest two1?+ excited states of FH molecule and lowest two3?g states of F2 molecule

A formalism of MRCPA(4) presented in the recent study of one of the authors (K. T.) and Mochizuki is reconsidered and coupling terms which appear in calculating excited states will be improved for the sake of guaranteeing size consistency in case of separating a molecular system into two fragments. The method is applied to calculating adiabatic potential curves of the lower three 1Σ+ states of the FH molecule and the lowest two 3Πg states of the F2 molecule. They include avoided crossing between Rydberg and valence-type states. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 661–668, 1999

A novel sialic acid binding site on factor H mediates serum resistance of sialylated Neisseria gonorrhoeae.

Factor H (fH), a key alternative complement pathway regulator, is a cofactor for factor I-mediated cleavage of C3b. fH consists of 20 short consensus repeat (SCR) domains. Sialic acid binding domains have previously been localized to fH SCRs 6-10 and 13. To examine fH binding on a sialylated microbial surface, we grew Neisseria gonorrhoeae in the presence of 5'-cytidinemonophospho-N-acetylneuraminic acid, which sialylates lipooligosaccharide and converts to serum resistance gonococci previously sensitive to nonimmune serum killing. fH domains necessary for binding sialylated gonococci were determined by incubating organisms with recombinant human fH (rH) and nine mutant rH molecules (deletions spanning the entire fH molecule). rH and all mutant rH molecules that contained SCRs 16-20 bound to the sialylated strain; no mutant molecule bound to serum-sensitive nonsialylated organisms. Sialic acid was demonstrated to be the fH target by flow cytometry that showed a fourfold increase in fH binding that was reversed by neuraminidase-mediated cleavage of sialic acid off gonococci. Functional specificity of fH was confirmed by decreased total C3 binding and almost complete conversion to iC3b on sialylated gonococci. Sialic acid can therefore bind fH uniquely through SCRs 16-20. This blocks complement pathway activation for N. gonorrhoeae at the level of C3.

Density functional study of hydrogen-bonded systems: Energetic and vibrational features of some gas-phase adducts of hydrogen fluoride

A series of detailed density functional calculations on hydrogen-bonded gas-phase adducts of the FH molecule for which both experiments and calculations based on traditional approaches were available have been carried out. The adducts were: (FH) 2, FH/CO and FH/NH 3. The adopted methods were: SCF, MP2, S-VWN, B-LYP, B-P86 and B3-LYP. Basis sets were: 6-31G(d,p), 6-31+G(d,p), 6-311++G(d,p), 6-311+G(2d,2p), 6-311+G(3df,2pd), DZ(d,p), cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ. Computed properties were: geometries, harmonic vibrations, binding energies and intensity of the F–H stretching mode of the donor. A detailed analysis of the anharmonicity associated with the F–H stretching mode was also carried out by numerically solving the nuclear Schrödinger equation associated with the F–H mode for both the FH/NH 3 and FH/CO cases. Comparison with previous studies as well as with available experimental data shows that heats of formation computed with the gradient corrected DF methods are as accurate as MP2 or better, when a basis set of at least triple-zeta valence quality with a double set of polarization functions is chosen. All functionals are able to give the correct order of stability for the FH/CO adduct, i.e. the carbon-bound structure as the more stable one, in agreement with MP2 studies. The Pople basis set 6-311+G(2d,2p) appears as good as the correlation-consistent basis set proposed by Dunning, namely aug-cc-pVDZ. Some care should be taken when adopting the 6-31G(d,p) basis set, as for instance in the case of (FH) 2 where spurious interactions stabilize cyclic structures with respect to open ones. All DF methods overestimate the shifts in the F–H stretching mode due to the hydrogen-bond interaction, calculated at the harmonic level, and no improvement is brought about by anharmonicity. The increase in the infrared intensity of the FH donor molecule is correctly accounted for. DF methods based on local electron density overestimate both the binding energies and the shifts in the F–H stretching mode showing their unrealiability for studying hydrogen-bonding interactions.

Reconciling simplicity and accuracy: compact valence bond wave functions with breathing orbitals

A method is proposed for computing compact ab initio valence bond wave functions suitable for diabatic states, or adiabatic states in case the interpretation of the wave function in terms of Lewis structures is needed. The method aims at combining the properties of interpretability and compactness of the classical valence bond method with a reasonable accuracy of the energetics. All Lewis structures relevant to the electronic system are generated, each of them being described by a single valence bond configuration state function. A balanced description of the different Lewis structures is ensured by allowing each configuration to have its specific set of orbitals during the optimization process. The method is applied to the F 2 and FH molecules and to the F 2 −, (NH 3) + 2 and Cl 2 − radicals to test its ability to reproduce equilibrium bond lengths and bonding energies for two-electron and odd-electrons bonds. Satisfactory results are obtained in all cases, despite the simplicity of the wave function which is composed of only two or three configurations. The dynamic electron correlation is shown to closely correspond to the instantaneous adaptation of the orbitals to the charge fluctuation that occurs in the two-electron bond, and more importantly in odd-electron bonds.

Accurate quantum Monte Carlo calculations for hydrogen fluoride and the fluorine atom

Quantum Monte Carlo calculations of the ground state energies of the fluorine atom and the hydrogen fluoride molecule have been carried out using both fixed-node and released-node methods. The fixed-node total energies for both F and FH are among the most accurate available. The fixed-node dissociation energy De=141.3(4) kcal mol−1 is in excellent agreement with experimental data. The cancellation of the nodal error was achieved with trial wave functions having nodal surfaces determined by Slater determinants of the near Hartree–Fock limit quality. With the released-node Green’s function quantum Monte Carlo method the lowest upper bounds to the ground state energies to date for both F [E0=−99.731(4) Hartree] and FH [E0=−100.458(5) Hartree] have been obtained.

Accurate small split-valence 3-21SP and 4-22SP basis sets for the first-row atoms

Split-valence Gaussian 3-21SP and 4-22SP basis sets are presented for the ground states of the first-row elements of the Periodic Table. The total energies of the atoms calculated with the new basis sets are significantly lower than those obtained with the well-known 3-21G and 4-31G basis sets. This is the consequence of the fact that the 3-21G and 4-31G basis sets do not correspond to the global minimum of the energy functional in the Hartree-Fock approximation. It is also shown that the 4–22 contraction scheme better corresponds to the solution structure of the Hartree-Fock equations with uncontracted 8s4p basis sets, and therefore permits one to obtain lower total energies than with the 4–31 contraction scheme. The proposed basis sets are tested by performing geometry optimizations and calculating the normal frequencies for the LiH, BeH 2, BH 3, CH 4, NH 3, OH 2, and FH molecules within the Hartree-Fock approximation.

Accurate atomic Gaussian basis functions for first-row atoms. Part 1. Contracted basis sets derived from 9s5p primitives

Contracted Gaussian basis sets (9s5p/5s3p), (9s5p/5s2p), (9s5p/4s2p), (9s5p/3s2p) and (10s5p/4s2p), (10s5p/3s2p) are presented for the ground states of the first-two atoms of the periodic table. The primitive basis (10s5p) is derived from a (9s5p) Gaussian basis by doubling one s-type function. A two-step procedure is applied for the construction of all basis sets reported. The atomic total energy is first optimized in the SCF approximation with respect to atomic exponential parameters and then with respect to the contraction coefficients. The energy functional is determined with a maximal error of less than 1.0 × 10 −8 E h in both cases. The basis sets are further tested by performing geometry optimizations of the LiH, BeH 2, BH 3, CH 4, NH 3, OH 2 and FH molecules at the Hartree-Fock level.

Theoretical value of the enthalpy of formation of methyl fluoride

The enthalpy of formation of CH 3F was theoretically estimated using the isogyric and hydrogenation reactions as working chemical reactions. Energy differences were computed at four levels of calculation, using the MP4, QCI and CC methods and two extended basis sets. Using the well-established enthalpy of formation of the FH molecule, the quality of the basis sets and energy correlation levels were tested. The value obtained was Δ H f,298K = −57.4 ± 1.2 kcal mol −1 (Δ H f,0K = −55.5 ± 1.2).

Adding the linked contributions of Triples and Quadruples to a size-consistent Singles and Doubles CI

A convenient procedure has been proposed recently to insure the size-consistence of Singles and Doubles CI; the method goes through a self-consistent dressing of the energies of the excited determinants which incorporates the unlinked effects of the Triples and Quadruples. Two strategies are proposed here to add thelinked contributions of the Triples and Quadruples, either by an perturbative MP-type calculation of these effects, or by a redefinition of the dressing of the SD-CI matrix. Test calculations on Be2, FH, NH3 and F2 molecules show that both methods efficiently approach the Full CI results (error ∼ 1 kcal mol−1). The second one satisfactorily treats the single-bonds breaking. It is finally shown that the effect of the T-Q linked effects may be efficiently approximated by truncating the MO basis set to the most occupied virtual quasi-natural MOs.

Molecular hyperpolarizabilities

We report a systematic study of the first and second hyperpolarizabilities of several small molecules at a consistent level of theory and basis sets. Coupled cluster (CC) methods for correlation, analytical high-order time dependent Hartree–Fock (TDHF) theory for dispersion effects, and polarizability-consistent basis sets give agreement to about 10% between the calculated hyperpolarizabilities and the gas phase experiments for the nonpolar molecules, H2, N2, CO2, and C2H4, and effectively nonpolar CO. Results for the polar molecules FH, H2O, NH3, and H2S are improved by adding lone-pair basis functions. For H2O and NH3 there is good (∼10%) agreement with experiment. However, a ∼20% difference between experiment and theory for the FH molecule persists; this difference is discussed in some detail.