Quantum mechanical studies of environmental effects on biomolecules

LCAO SCF calculations with a (7s, 3p/3s) atomic basis are performed on urea and hydrated urea in order to determine the preferred sites of water fixation using the supermolecule approach. It appears that up to five water molecules can be directly bound to urea in the first hydration shell.     

A theoretical study of electrophilic reactions

The electronic structures of protonated formyl and acetylium cations and their deprotonation paths leading to HCO⁺, COH⁺ and CH₃CO⁺have been studied by means of ab initio calculations. The results support Olah's theory that dipositive species can be the de facto reagents in electrophilic reactions.     

A simulation of the exchange potential in unrestricted and restricted Hartree-Fock calculations studied on atoms

The spherical average of the Hartree-Fock exchange potential depending on each spin orbital is compared with Slater's exchange potential, V _xs, as demonstrated for the phosphorus atom. It is shown that the former potential can be simulated by (a + br)V _xs, where r is the radius and the constants a and b are calculated for each spin orbital. This simulation is tested for the iron atom and it is found that the results agree well with those obtained from unrestricted and restricted Hartree-Fock calculations, respectively. The applicability of this new method in energy band structure calculations is briefly discussed.Dedicated to Professor H. Hartmann on the occasion of his 65th birthday.     

Conformational analysis of dimethylphosphate with quantum-mechanical and classical methods

In order to shed light on the conformational behavior of polynucleotide chains, and in particular to clarify the origins of the barriers to internal rotation in the phosphodiester linkage, we computed, with a quantum-mechanical ab initio procedure, the energies associated to 86 combinations of the two torsion angles in the dimethylphosphate anion (CH₃O)₂PO₂ ^–, and then we sought for an analytical expression apt to reproduce these energies with the highest possible accuracy. An excellent agreement (standard deviation of the fitted energies from the ab initio energies 0.28 kcal/mole) with the quantum-mechanical calculations was reached with a potential consisting of four terms: 1) a 6–12 Lennard-Jones contribution, in which different parameters are used to describe the interactions of methyls with the ester oxygens and with the anionic oxygens; 2) a contribution with twofold periodicity, accounting for the anomeric effects connected to the interactions between the lone pair electrons and the polar bonds of phosphorus with the anionic oxygens; 3) a contribution with threefold periodicity, representing the usual bond-staggering term; and 4) a Coulombic contribution, arising from electrostatic interactions between partially charged atoms.     

Quantum-mechanical exploration of the properties of the sugar rings

Theab initio SCF method is used for computing the main electronic properties of the ribose unit of the nucleic acids. The present study is devoted to the ribose in the C₃-endo,gg conformation. The properties investigated include the distribution of the electronic charges, the electrostatic molecular potential around the four oxygens of the unit, the hydration and the Na⁺ binding schemes studied in the supermolecule approximation. The possibilities of through-water binding of the cation to the sugar are also explored. The predictions of the computation in particular with regard to cation binding to the ribose ring are correlated with recent experimental results.     

Studies of the energy spectrum of α, ω- substituted polymethine chains. II. Polymethine chains with odd number of methine groups

The analysis of the experimental data for the energy of the longest wavelength optical transitions _n,opt of substituted polymethines X (CH)_2n+1 X shows that in the asymptotic case (n) _,opt does not tend to zero, as it follows from the empirically established correlations, but has a finite, non-zero value. It is shown that the energy gap of odd polymethines is the same as that of the even polymethines - the polyenes (E 2 eV). The substituents (X N, O, B) are responsible for the appearance of levels in the gap. These, depending on the substituent character, are vacant (X B) or occupied (X N, O). The transition from or to such a level determines the longest wavelength optical transition energy of polymethines.     

Ab initio crystal orbital studies on linear chains of H atoms

Anab initio crystal orbital method is used to calculate the energies of an infinite chain of H atoms and of linear arrangements of H₂ molecules with different interatomic distances. The H₂ arrangements are not stable in respect to isolated molecules. The cohesive energy of an optimized arrangement of H atoms chain is 0.0354 a.u.     

Non-additivity in water-ion-water interactions

The three-body system Li⁺(H₂O)₂ was analyzed to study that non-additive part of the interaction potential which can be obtained by the Hartree-Fock approximation.For long and intermediate distances the three-body correction was found to be well represented by the induction energy, where bond dipoles are induced on each water molecule by point charges located on the (unpolarizable) lithium ion and on the other molecule respectively: for shorter distances this approximation was corrected by means of an exponential repulsive term. Such a potential model for non-additive interactions was extended to the more general situation Li⁺(H₂O)_n, and Monte-Carlo calculations were carried out on clusters containing up to six water molecules; comparison with other simulation results and with available data showed a significantly improved agreement with experiment. Tentative values for H are presented for n =7, 8,..., 20, where experimental data are not available.     

Numerical integration of overlap and ligand contributions to the electric field gradient

The total electric field gradient (EFG) tensor V _pq is calculated by numerical integration of threedimensional integrals. Each of them is solved a) by integrating over one dimension analytically and b) by integrating over the remaining two dimensions on the basis of a Gauss-type integration rule. The use of 100 abscissas in the twodimensional numerical integration scheme yields satisfactory accuracy which was checked by evaluating overlap integrals; an increase to 400 abscissas does not increase the result drastically. Calculating quadrupole splittings E _Q from numerically integrated electric field gradient tensors V _pq we observe that depending a) on the amount of covalency and b) on the amount of deviation from octahedral or tetrahedral symmetry, involved in a molecular system, overlap and ligand contributions to V _pq play an important role. Especially for the sandwich compound ferrocene, Fe(C₅H₅)₂, we find a significant difference between E _Q ^{num. int.} which follows from the numerical integration method, and E _Q ^conventional which is derived from effective charges.Supported by Deutsche Forschungsgemeinschaft     

A non-empirical molecular orbital study on the relative stabilities of adenine and guanine tautomers

The relative stabilities of a series of adenine and guanine tautomers have been calculated using anab initio Hartree-Fock-Roothaan SCF MO method. The calculated relative stabilities agree in general with the results of earlier semiempirical studies. According to the present study, tautomeric forms with regular Kekulé structure for the six-membered purine ring are the most stable. The amine-imine tautomerization of purine bases is not likely to be responsible for spontaneous mutations in DNA.     

Iterative natural orbitals for configuration interaction using perturbation theory

Approximate natural orbitals are determined iteratively from CI expansions constructed using first-order perturbation theory in order to investigate the possibility of eliminating the complete transformation of MO integrals on each iteration. Results on LiH and H₂O are compared with fully variationally determined NO's to assess questions of convergence.     

On the sites and mechanisms of alkylation in the nucleic acids

The intrinsic capacity (computed by ab initio molecular orbital techniques) of ethyl and methyl cations to bind to the anionic oxygens of the phosphate groups of the nucleic acids is found to be larger than their affinity for the carbonyl oxygens or for the nitrogens of the bases cytosine and guanine. Analysis of the components of the binding energies indicates that the preference of the ethyl cation for the oxygens of the phosphate or for those of the bases is due to different reasons. The results are discussed in connection with the available experimental observations.     

Complementary molecular orbital investigations on the conformation of choline derivatives

Quantum-mechanical computations by the PCILO method, applied previously to the study of the conformational properties of acetylcholine and its derivatives modified in the central part of this molecule, are extended to modifications involving its cationic head and its ester terminal. The replacement of the methyl groups of the cationic head by hydrogens or ethyl groups leads to a steep decline in parasympathomimetic activity. It is shown that the triethyl derivative conserves the gauche form as the most stable one. The redistribution of the electronic charges at the onium group implies, however, a transition from an ionic to a hydrophobic binding. The replacement of the methyls by two or three hydrogens leads to a different preferred gauche-gauche conformation. The replacement of the methyl group at the ester terminal by a phenyl ring enables a comparison with the conformational properties of local anesthetics. The study brings about evidence, substantiated by NMR spectroscopy, that acetylcholine analogs and protonated local anesthetics are conformationally similar. Choline ethers also show a general preference for a gauche conformation. Nevertheless, biological studies do not indicate a constant correlation between conformation and biological potency. Conformational analogies or discrepancies alone cannot thus account for the fine details of the biological activity which must depend also on the electronic structure.This work was supported by the A.T.P. N A 655-2303 of the C.N.R.S.     

Theoretical study of the electronic structure of diazomethane

The least-energy dissociation path of the ground state of CH₂N₂ was determined fromab initio calculations using in a complementary way basis sets of minimal size (STO-3G) and double-zeta (DZ) quality. The results indicate that the least-energy point of attack of the N₂ molecule on CH₂ (¹ A ₁) is roughly perpendicular to the molecular plane (93 °), the C and N atoms being almost co-linear (angle C-N-N203 ° with outermost N atom pointing away from CH₂). The potential barrier of 1.2 eV found previously on theC _2v dissociation path, disappears completely along the least-energy dissociation path (point groupC _s (out-of-plane)). These findings corroborate the Woodward-Hoffman rules for this process since the outermost orbitals of the two intersecting states found in point groupC _2v (...2b ₁ and ...8a ₁) both correlate to the same irreducible representation (10á) in point groupC _s (out-of-plane).Larger basis set calculations (DZ + polarization functions on all centers, 3d _c and 3d _N developed here), were also carried out on CH₂N₂ (¹ A ₁,³ A ₂ and¹ A ₂) at the¹ A ₁ equilibrium geometry and on CH₂ (³ B ₁) and N₂ (¹ _g ⁺ ) at their respective equilibrium geometries. These calculations, together with consideration of correlation energy differences, yieldD ₀ ⁰ (CH₂N₂,¹ A ₁) = 19 kcal/mole and vertical excitation energies of 67 and 73 kcal/mole for the³ A ₂ and¹ A ₂ states respectively. The latter value is in good agreement with the measured experimental value: 72.4 kcal/mole corresponding to the maximum of intensity in the¹ A ₂¹ A ₁ absorption band.     

Cation-binding to biomolecules

Ab initio SCF computations indicate that Mg²⁺ should bind essentially to the oxygen atoms of uracil, the remaining part of the base being rather repulsive towards such an interaction. The Coulombic component predominates in the interaction, the essential feature of which may thus be deduced from the study of the molecular electrostatic potential of uracil. These ab initio results contradict an earlier CNDO prediction that the binding of uracil and Mg²⁺ should occur preferentially at the C₅=C₆ double bond of the base. It is shown that the CNDO result is an artifact due to an exaggeration by this method of the charge transfer between the ligand and the cation. The small amount of available experimental data seem in favor of the ab initio results.     

Band structure of nonclassical polymers

It is shown that fully conjugated alternant nonclassical polymers are comparatively stable systems as a result of the considerable delocalisation energy.The energy characteristics of the polymers are strongly determined by the electron spin distribution of the degenerate nonbonding molecular orbitals; the full spin configuration,S>0, is favoured. The spin densities depend on the electron correlation and alternate; this corresponds to a ferrimagnetic state of the polymer at 0°K.     

Basis set dependence of localized orbitals

The effects of Gaussian basis set contraction and addition of polarization functions on H₂O localized orbitals have been studied at the experimental geometry. It is shown that the electric moments and moment features of localized orbitals are not influenced very much by basis set quality variations, as going from medium size to enlarged basis sets. The difference between bond pair and lone pair charge densities was found to be larger on approaching the Hartree-Fock limit. A minimal basis set, however, does not suitably characterize the localized charge distributions.     

The physical nature of the lone pair

Despite the large number of experimental and theoretical studies on the size, shape, and orientation of lone pairs and their resulting stereochemical character, lone pairs still remain poorly defined in terms of quantitative observable properties of a molecule. Using the conformation of saturated molecules and barriers to internal rotation, experimental chemists have arrived at conflicting sizes and orientations for lone pairs. Most theoretical attempts to define lone pair properties have centered on such non-observables as localized molecular orbitals or have been based on studies on isolated molecules.The use of observable properties to construct a consistent set of physical models to analyze the physical nature of lone pairs is discussed. Much as one probes an electric field with a test charge, probes such as H⁺, H^–, He and H could be used to probe regions of molecules such as NH₃ and H₂O where lone pairs are often postulated to exist.Ab initio quantum mechanical studies can be analyzed using electron density (and resulting changes during interaction), total pair density of electrons, the electrostatic potential about the molecule and bond energy analysis to study lone pair properties. A simple study of NH₃ using an H⁺ probe is presented to clarify the approach.     

Theoretical studies on the conformation of saccharides

Conformations of 2-methoxytetrahydropyran as a model for the six-membered ring in aldopyranosides have been calculated by the PCILO method using the algorithm of the conjugated gradient to optimize the geometry. The calculated geometry of the fourteen basic forms of 2-methoxytetrahydropyran was found to be in agreement with the available data obtained by X-ray diffraction of pyranosides. The results indicate differences in the geometry of 2-methoxytetrahydropyran resulting from the change of the axial vs. equatorial position of the methoxyl group. These changes are particularly meaningful in the values of bond angles and they are in agreement with the anomeric and exoanomeric effects. The experimentally found differences in the energies of an axial (⁴ C ₁) and equatorial (¹ C ₄) conformer, G = 2.9–3.7 kJ/mol, and the dipole moment, = 1.20 ± 0.05 D (1D = 3.33 10^–30mAs) agree well with the calculated values E = 3.18 kJ/mol and <> = 1.18 D which, in turn, suggest that the axial conformer is preferred over the equatorial one by a ratio a:e = 78:22.     

Ab initio study of hydrazoic acid

SCF and CI calculations were carried out on the ground^1A state of HN₃. The equilibrium geometry and vibration frequencies were computed. The results point to a planar structure (groupC _s) but to a non-linear (170 °) N-N-N conformation. The calculated vibration frequencies are in fair agreement with experimental assignments.The dissociation path of the molecule to NH and N₂ products was investigated and compared to the isoelectronic reaction of diazomethane. The dissociation energy of hydrazoic acid is estimated to be about –8 kcal/mole, with a potential barrier to dissociation of about 30 kcal/mole.Boursier IRSIA