Nonadditivity of secondary deuterium isotope effects on basicity of trimethylamine

Secondary deuterium isotope effects (IEs) on basicities of isotopologues of trimethylamine have been accurately measured by an NMR titration method applicable to a mixture. Deuteration definitely increases the basicity, by approximately 0.021 in the Delta pK per D. The IE is attributed to the lowering of the CH stretching frequency and zero-point energy by delocalization of the nitrogen lone pair into the C-H antibonding orbital. Because this depends on the dihedral angle between the lone pair and the C-H, a further consequence is a preference for conformations with H antiperiplanar to the lone pair and D gauche. This leads to a predicted nonadditivity of IEs, which is confirmed experimentally. It is found that the decrease in basicity, per deuterium, increases with the number of deuteriums. The nonadditivity of IEs is a violation of the widely assumed Rule of the Geometric Mean.     

The effect of conjugation on the magnitude of secondary alpha deuterium kinetic isotope effects

The unexpectedly small secondary alpha deuterium KIE in the 4-methoxybenzyl chloride-thiophenoxide ion reaction is attributed to the increased conjugation between the aryl group and the alpha carbon in the S_N2 transition state.     

A new method for the calculation of vibrational force constants. Application to H2

A new method for the quantum mechanical calculation of vibrational force constants is presented. This method is applied to the calculation of the vibrational force constant of H₂, using a completely optimized wavefunction constructed from a single gaussian orbital. The value of the force constant obtained using this method is k₀ = 0.422341088751 au (= 6.5754 × 10⁵ dyne/cm), compared to the value of k₀ = 0.42234079S380 au (= 6.5754 × 10⁵ dyne/cm) obtained using an analytic method, and the experimental value of k_e = 0.3692 au (= 5.748 × 10⁵ dyne/cm).     

A virtual vibrational self-consistent-field method for efficient calculation of molecular vibrational partition functions and thermal effects on molecular properties

A new method is described for the calculation of molecular vibrational partition functions and thermal effects on molecular properties including an explicit account of anharmonicity. The approach is based on the vibrational self-consistent-field method. Partition functions and thermal averages of the energies calculated with the new method are generally in good agreement with the result of more accurate methods. At lower temperatures the method gives in addition good results for thermal averages of dipole moments and polarizabilities. The new method is much more efficient than explicit sum-over-states approaches previously used for calculation of thermal averages. Unlike the standard sum-over-states approach, the newly developed method is feasible for larger systems despite the formal exponential increase in the number of states with the size of the system. Thus, it is presently the only practical way for including an explicit treatment of anharmonicity in vibrational wave function based calculations of molecular vibrational partition functions and thermally averaged properties of larger molecules.     

The kinetic method reveals secondary deuterium isotope effects on the proton affinity and gas-phase basicity of glycine and alanine methyl esters

The kinetic method for measuring proton affinities (PA) and gas-phase basicities (GB) was applied to the methyl esters of simple amino acids. The experiments show that the GB and PA values for deuterium labeled glycine methyl ester are indeed greater than that of the corresponding unlabelled glycine methyl ester. The PA of -Ala-OCD₃ is also slightly greater than that of the unlabeled alanine methyl ester. The secondary isotope effects originate, as shown by density functional theory, in differences in zero-point energies and thermal-energy corrections between H and D-bearing molecules.     

Application of Forst's method to the calculation of thermal unimolecular reaction rates and isotope effects in the falloff region

A method proposed in 1972 by W. Forst is used to calculate the experimentally accessible pressure dependence of thermal unimolecular rate constants. The specification of an activated complex always employed in RRKM calculations is avoided. This allows for a more consistent comparison between the results obtained by the application to various unimolecular processes. In order to bring experimental and calculated curves into agreement, fourcenter eliminations of hydrogen halides from alkyl halides require the formal introduction of a collision efficiency factor λ ? 0.2, and for the concerted ring opening of 1,1-dichlorocyclopropane λ ? 0.4 must be assumed. The isotope effects for the decomposition of CD₃CD₂Cl and CH₃CD₂Cl have been studied, and the pressure dependence of k_H/k_D is reported. Studying the biradical ring opening of oxetan, cyclobutane, and cyclopropane, the falloff curves and isotope effects are predicted within the experimental uncertainty by the use of λ ? 1.0. This different behavior of concerted and biradical reactions against falloff calculations can hardly be attributed to experimental uncertainties in the Arrhenius parameters and/or the collision frequency alone.     

Cation effects on the vibrational frequencies of adsorbed thiocyanate on platinum

Infrared spectra of thiocyanate adsorbed on a platinum electrode surface were obtained in the presence of perchlorate electrolytes of various alkali metal cations. It was discovered that the vibrational frequency of the C-N stretching mode is dependent upon the nature of the supporting electrolyte cation. Two bands were observed in the 2050 to 2150 cm⁻¹ range; one band was attributed to nitrogen-bound thiocyanate, and the other to species adsorbed via the sulfur atom. Each of these bands demonstrated independent frequency dependencies on cation nature and on the applied electric field within the interfacial region. Differences were also observed in the intensity dependence of the bands on the applied potential. The results were explained in terms of changes in the distance between the outer Helmholtz plane (OHP) and the surface of the electrode, and also in terms of the possible influence of coadsorbed alkali metal cations on the vibrational frequency of thiocyanate species adsorbed through the nitrogen atom. The effects that variations in the OHP-electrode distance impart on the magnitude of the potential drop across the interface, and the influence of small changes in this potential field on the C-N stretching frequency of N- and S-adsorbed thiocyanate species, are discussed.     

Approaches for the calculation of vibrational frequencies in liquids: comparison to benchmarks for azide/water clusters

Ultrafast vibrational spectroscopy experiments, together with molecular-level theoretical interpretation, can provide important information about the structure and dynamics of complex condensed phase systems, including liquids. The theoretical challenge is to calculate the instantaneous vibrational frequencies of a molecule in contact with a molecular environment, accurately and quickly, and to this end a number of different methods have been developed. In this paper we critically analyze these different methods by comparing their results to accurate benchmark calculations on azide/water clusters. We also propose an optimized quantum mechanics/molecular mechanics method, which for this problem is superior to the other methods.     

Multidimensional anharmonic calculation of the vibrational frequencies and intensities for the trans and cis isomers of HONO with the use of normal coordinates

The equilibrium geometry and the potential energy and dipole moment surfaces have been determined for the cis and trans isomers of the HONO molecule by an ab initio Moller–Plesset (MP2) calculation with a wide set of atomic orbitals. The multidimensional anharmonic vibrational Schrodinger equations are solved using the variational method with the Hamiltonian and wave functions written in the normal coordinates of cis and trans isomers. All one- and two-dimensional and a number of three-dimensional vibrational problems are solved to obtain the energy levels and vibrational eigenfunctions. The frequencies and intensities for the fundamental, overtone and some combination bands are determined in good agreement with the available experimental results. The calculation shows the strength of coupling between different vibrational modes and reveals the presence of strong resonances between the (v₁, v₃, v₆) and (v₁, v₃−1, v₆+2) states of cis-HONO. This fact may be important for understanding the energy redistribution between the intermolecular degrees of freedom. The magnitude and direction of vibrationally averaged ground-state dipole moment of both isomers, as well as the direction of transition dipole moments, are in good agreement with the experimental findings. The changes in the values of dipole moment and some geometrical parameters of cis- and trans-HONO on vibrational excitation are also computed.     

Intramolecular deuterium isotope effects in the meta photocycloaddition of aromatic compounds to alkenes

The effect of substitution of hydrogen by deuterium in some aromatic compounds on product distributions in the meta photocyloaddition to alkenes was investigated. The isotope effects found are in agreement with a polar mechanism.     

Solvent and deuterium isotope effects on the decomposition of ammonium nitrite solutions

The rate of decomposition of NH₄NO₂ solutions, at pH 5–7, equals k[NH₃] [HNO₂]² or k[NH ₄ ⁺ ] [NO ₂ ^– ][HNO₂]. A plausible mechanism involves a ratedetermining attack of N₂O₃, derived from HNO₂, on NH₃. H⁺⁺ and S⁺⁺ are 82 kJ-mol^–1 and –27 J-mol^–1-K^–1, respectively. On partially replacing the solvent water by methanol or ethanol, the change G⁺⁺, coupled with the calculated standard Gibbs energy of transfer of the reactants from water to the mixed solvent indicated that, in the latter, there is a greater destabilization of the transition state compared to that of the reactants. This can be explained by assuming two hydrogen bonds from the same water molecule to the transition state and hence a loss of hydrogen bond energy in the mixed solvent compared to the aqueous solution. The rate constant for the reaction of ND₄NO₂ in D₂O compared to the reaction of NH₄NO₂ in water, gave a composite isotope effect involving two acid-base equilibria, suggested in the proposed mechanism; in addition to primary isotope effects in the equilibrium: 2 HNO₂N₂O₃+H₂O.     

An effective scaling frequency factor method for scaling of harmonic vibrational frequencies: Application to 1,2,4-triazole derivatives

Scaling of harmonic frequencies of a molecule is one of the methods of improving the agreement between the calculated from a quadratic force field and experimental vibrational spectrum. An application of the recently proposed effective scaling frequency factor (ESFF) method to the complicated 1,2,4-triazole derivatives is presented. The calculations are based on the DFT/B3LYP/6-311G** quadratic force fields. It is shown that the ESFF method is capable of providing the high-quality spectra with regard to the scaled frequencies, comparable to these obtained with the well-established scaled quantum mechanical (SQM) force field method. Using the recommended scaling factors for the 11-parameter calculations, the RMS value obtained for a set of 293 vibrational modes of four compounds is only 8.7 and 8.5 cm^?1, for SQM and ESFF, respectively, provided the hydrogen bonded CO bond was excluded from the general non-hydrogen XX stretch group, and the scaling factor attributed to this bond was optimized. The new, 9-parameter set of scaling factors provides SQM- and ESFF-scaled frequencies that are of comparable quality to those of the 11-parameter calculations. In addition, it provides (on average) more reliable band splittings in the middle region of the spectrum, and the order of the scaled frequencies corresponds to that of the experimental bands. The straightforward application of the ESFF method to estimate the value of the scaled frequency is also presented.     

Secondary deuterium isotope effects on the acidity of carboxylic acids and phenols

Secondary deuterium isotope effects (IEs) on acidities have been accurately measured by an NMR titration method applicable to a mixture of isotopologues. Deuteration definitely decreases the acidity of carboxylic acids and phenols, by up to 0.031 in the DeltapK per D. For aliphatic acids, the IEs decrease as the site of deuteration becomes more distant from the OH, as expected, but a surprising result is that IEs in both phenol and benzoic acid do not decrease as the site of deuteration moves from ortho to meta to para. The experimental data are supported by ab initio computations, which, however, substantially overestimate the IEs. The discrepancy does not seem to be due to solvation. The IEs originate in isotope-sensitive vibrations whose frequencies and zero-point energies are lowered upon deprotonation. In the simplest case, formate, the key vibration can be recognized as the C-H stretch, which is weakened by delocalization of the oxygen lone pairs. For the aromatic acids, delocalization cannot account for the near constancy of IEs from ortho, meta, and para deuteriums, but the observed IEs are consistent with calculated vibrational frequencies and electron densities. Moreover, the ability of the frequency analysis to account for the IEs is evidence against an inductive origin.     

Direct calculation of lattice sums. A method to account for the crystal field effects

A method of direct calculation of lattice sums in three-dimensional crystals is reported. The method is based on annihilation of some lowest multipole moments of the unit cell by a redefinition of the unit cell content. As a result, properties of the infinite crystal can be calculated as usual by taking a finite cluster of unit cells, but surrounded by an additional surface layer of a charge density (e.g., a layer of point charges). This charge density distribution produces the electric field approximating that one of the rest of the infinite crystal. The method proposed is easily applicable in the SCFLCAO procedure as well as in any method using a cluster representation for an infinite crystal. The validity of the infinite crystal model for a finite crystal is also discussed.     

A systematic and efficient method to estimate the vibrational frequencies of linear peptide and protein ions with any amino acid sequence for the calculation of rice-ramsperger-kassel-marcus rate constant

A systematic method to automatically estimate the vibrational frequency sets of linear peptide and protein ions with any amino acid sequence, which is needed in Rice-Ramsperger-Kassel-Marcus (RRKM) calculations for dissociation of these ions, has been developed. The method starts from the frequencies of free amino acids calculated quantum chemically at the DFT/B3LYP/6-31G** level. Some of these were systematically eliminated to get fictitious sets of frequencies for each amino acid at the C-terminus, N-terminus, and inside the chain. By collecting these sets as needed for a specified amino acid sequence and adding vibrations appearing upon peptide bond formation and protonation, a complete set of vibrational frequencies was obtained. Other conditions for RRKM calculations have also been systematically specified. RRKM calculations performed under various conditions have shown that the present method can be useful for an order of magnitude estimation of a statistical rate constant even at low internal energy region. The fact that arbitrariness involved in constructing an entire frequency set simply through spectral correlation can be avoided, and that any protein ion can be handled systematically and rapidly once its sequence and the number of protons attached are specified, are the main advantages of the present method.     

The impact of approximate VSCF schemes and curvilinear coordinates on the anharmonic vibrational frequencies of formamide and thioformamide

The accuracy of the vibrational self-consistent field (VSCF) method for the computation of anharmonic vibrational frequencies in the infrared (IR) spectrum of formamide and thioformamide is investigated. The importance of triple potentials in the commonly used hierarchical expansion of the potential energy surface (PES) is studied in detail. The PES is expanded in terms of Cartesian as well as internal coordinate normal mode displacements. It is found that triples play an important role when using rectilinear coordinates. A VSCF computation based on rectilinear displacements exhibits serious shortcomings which are only remedied by a large vibrational configuration interaction (VCI) treatment including triple potentials. These limitations are partially removed when using curvilinear coordinates. The merits and disadvantages of either type of displacements for the generation of the PES are discussed.