Zero-point Effects Research Articles

Heats of formation for [formula omitted

The dissociation energies of Fe(CO) n ( n=2–4) are computed using correlation consistent basis sets and the CCSD(T) approach. The dissociation energies are extrapolated to the CBS limit and are corrected for core–valence (CV), scalar relativistic, spin–orbit, zero-point, and thermal effects. Our iron carbonyl bond strengths agree with experiment within the respective error bars. We use our dissociations energies at 298 K to obtain the heats of formation of Fe(CO) n ( n=1–4).

A converged calculation of the energy barrier to internal rotation in the ethylene–sulfur dioxide dimer

Geometrical parameters for the equilibrium (MIN) and lowest saddle-point (TS) geometries of the C2H4⋯SO2 dimer, and the corresponding binding energies, were calculated using the Hartree–Fock and correlated levels of ab initio theory, in basis sets ranging from the D95(d,p) double-zeta basis set to the aug-cc-pVQZ correlation consistent basis set. An assessment of the effect of the basis set superposition error (BSSE) on these results was made. The dissociation energy from the lowest vibrational state was estimated to be 705±100 cm−1 at the basis set limit, which is well within the range expected from experiment. The barrier to internal rotation was found to be 53±5 cm−1, slightly higher than the (revised) experimental result of 43 cm−1, probably due to zero-point vibrational effects. Our results clearly show that, in direct contrast with recent ideas, the BSSE correction affects differentially the MIN and TS binding energies and so has to be included in the calculation of small energy barriers such as that in the C2H4⋯SO2 dimer. Previous reports of positive MP2 frozen-core binding energies for this complex in basis D95(d,p) are confirmed. The anomalies are shown to be an artifact arising from an incorrect removal of virtual orbitals by the default frozen-core option in the GAUSSIAN program.

The Substrate Reaction Mechanism of Class III Anaerobic Ribonucleotide Reductase

The substrate mechanism of class III anaerobic ribonucleotide reductase has been studied using quantum chemical methods. The study is based on the previously suggested mechanism for the aerobic class I enzyme, together with the recently determined X-ray structure of the anaerobic enzyme. The initial steps are similar in the mechanisms of these enzymes, but for the suggested rate-limiting steps there are key differences. In the class I enzyme, the 3 ' -keto group of the substrate is protonated in a step involving formation of a sulfur-sulfur bond between two cysteines, One of these cysteines is not present in the anaerobic enzyme. Instead, carbon dioxide is formed in this step from formate, which is present as a cofactor. In line with previous suggestions from experimental observations, the formate first forms a formyl radical. The next step, where the formyl radical protonates the 3 ' -keto group of the substrate, is suggested to be rate limiting with a calculated total barrier of 19.9 kcal/mol, in reasonable agreement with the experimental rate-limiting barrier of 17 kcal/mol. Zero-point and entropy effects are found to be quite significant in lowering the barrier. The mechanism for the entire cycle is discussed in relation to known experimental facts.

The Cotton–Mouton effect of gaseous CO2, N2O, OCS, and CS2. A cubic response multiconfigurational self-consistent field study

The hypermagnetizability and the hypermagnetizability anisotropy of CO2, N2O, OCS, and CS2 are computed at a wavelength of 632.8 nm using cubic response theory with multiconfigurational self-consistent field wave functions. The anisotropies of the electric dipole polarizability and of the magnetizability are also obtained. This allows us to study the temperature dependence of the Cotton–Mouton constant for all four molecules and thus to compare to the results of the experimental study by Kling and Hüttner [Chem. Phys. Lett. 90, 207 (1984)]. We also assess the importance of pure and zero-point vibrational effects on the relevant molecular properties. In particular, we show that for CO2, OCS, and CS2, the pure vibrational effects to the hypermagnetizability anisotropy can be even more important than the electronic contribution.

Zero-point vibrational effects on optical rotation

We investigate the effects of molecular vibrations on the optical rotation in two chiral molecules, methyloxirane and trans-2,3-dimethylthiirane. It is shown that the magnitude of zero-point vibrational corrections increases as the electronic contribution to the optical rotation increases. Vibrational effects thus appear to be important for an overall estimate of the molecular optical rotation, amounting to about 20–30% of the electronic counterpart. We also investigate the special case of chirality introduced in a molecule through isotopic substitution. In this case, the zero-point vibrational effects are the only source of optical activity, and we investigate the magnitude of these effects through calculations on mono-deuterated oxirane.

First principles study of isotope effect in hydrogen-bonded K 3H(SO 4): : II — Zero-point oscillation effect

First principles calculation is performed to find the difference between K 3H(SO 4) 2 (KHS) and K 3D(SO 4) 2 (DKHS) by taking account of the zero-point oscillation effects of the proton and the deuteron. First, we calculate the potential surface for the proton in the crystal. The ground-state energies and the wavefunctions of the proton and the deuteron in that potential are calculated. Then, the stable positions of the proton and the deuteron are calculated taking account of zero-point energy, and the electric charge distributions are calculated taking account of the spread wavefunctions of the proton and the deuteron. As a result, we find that the anharmonicity of the proton potential surface makes the position of the hydrogen closer to the center of the hydrogen bond than that of the deuterium. We also find that the zero-point oscillation effect diminishes the dipole moments, and that the shrinkage of the dipole moment in the hydrogen system is larger than that of the deuteron. These two effects play significant roles in the mechanism of the isotope effect in KHS.

Ab Initio Calculations on the 5-exo versus 6-endo Cyclization of 1,3-Hexadiene-5-yn-1-yl Radical: Formation of the First Aromatic Ring in Hydrocarbon Combustion

Two possible reaction pathways between 1,3-hexadien-5-yn-1-yl radical (1) and phenyl radical (2), a key reaction in soot formation during fuel combustion processes, have been investigated using ab initio quantum mechanical electronic structure calculations. The complete active space (CAS) SCF method was used for geometry optimization of the equilibrium and transition-state structures relevant to the two competing mechanisms and computing their harmonic vibrational frequencies. Final energies were evaluated by single-point calculations using essentially the G2M(RCC,MP2) method and corrected for zero-point and temperature effects. According to all calculated barrier heights (ΔU⧧ , ΔE⧧ , ΔH⧧ , and ΔG⧧ ) the 5-exo cyclization of 1 to (2,4-cyclopentadienyl)vinyl radical (3) is favored over the 6-endo cyclization to 2. As in the case of the prototypical hex-5-enyl radical, the predicted highly regioselective 5-exo cyclization of 1 is due to favorable enthalpic and entropic factors associated with the formation ...

Structures, energies, vibrational spectra, and electronic properties of water monomer to decamer

The correlation of various properties of water clusters (H2O)n=1–10 to the cluster size has been investigated using extensive ab initio calculations. Since the transition from two dimensional (2-D) (from the dimer to pentamer) to 3-D structures (for clusters larger than the hexamer) is reflected in the hexamer region, the hexamer can exist in a number of isoenergetic conformers. The wide-ranging zero-point vibrational effects of the water clusters having dangling H atoms on the conformational stability by the O–H flapping or proton tunneling through a small barrier (∼0.5 kcal/mol) between two different orientations of each dangling H atom are not large (∼0.1) kcal/mol). Large dipole moments (>2.5 D) are found in the dimer and decamer, and significant dipole moments (∼2 D) are observed in the monomer, hexamer, and nonamer. The polarization per unit monomer rapidly increases with an increasing size of the cluster. However, this increase tapers down beyond the tetramer. The O–H vibrational frequencies serve as sensitive indicators of the status of proton donation (“d”) and acceptance (“a”) (i.e., the structural signature of H-bond type) for each water monomer in the cluster. In general, the magnitudes of the O–H frequencies (ν) for each cluster can be arranged in the following order: ν3da (single donor–single acceptor) ≅ν3daa (single donor–double acceptor) >ν3dda (double donor–single acceptor) >ν1dda>ν1da> (or ≅) ν1daa. The increase in the cluster size has a pronounced effect on the decrease of the lower frequencies. However, there are small changes in the higher frequencies (ν3da and ν3daa). The intensities of ν1daa and ν1da are very high, since the increased atomic charges can be correlated to the enhanced H-bond relay effect. On the other hand, the intensities of the ν1dda modes are diminished by more than half. Most of the above data have been compared to the available experimental data. Keeping in view the recent experimental reports of the HOH bending modes, we have also analyzed these modes, which show the following trend: ν2dda>ν2daa≅ν2da. The present study therefore would be useful in the assignments of the experimental O–H stretching and HOH bending modes.

Noble gas–metal chemical bonding? The microwave spectra, structures, and hyperfine constants of Ar–CuX(X=F, Cl, Br)

The rotational spectra of the complexes Ar–CuF, Ar–CuCl, and Ar–CuBr have been observed in the frequency range 5–22 GHz using a pulsed-jet cavity Fourier transform microwave spectrometer. All the complexes are linear and rather rigid in the ground vibrational state, with the Ar–Cu stretching frequency estimated as ∼200 cm−1. Isotopic data have been used to calculate an r0 structure for Ar–CuF, while for Ar–CuCl and Ar–CuBr partial substitution structures have also been obtained. To reduce zero-point vibrational effects a double substitution method (rd) has also been employed to calculate the structures of Ar–CuCl and Ar–CuBr. The Ar–Cu distance has been found to be rather short and to range from 2.22 Å in Ar–CuF to 2.30 Å in Ar–CuBr. Ab initio calculations at the MP2 level of theory model the geometries and stretching frequencies well and predict an Ar–Cu bond energy in Ar–CuF of ∼47.3 kJ mol−1. Large changes in the Cu nuclear quadrupole coupling constant on complex formation show that extensive charge rearrangement occurs upon formation of the complexes. This, in conjunction with the sizable dissociation energy, suggests that the Ar–Cu bonds in these complexes are weakly covalent. The rotational spectrum of CuF has also been reinvestigated to improve the hyperfine constants.

The microwave spectra and structures of Ar–AgX (X=F,Cl,Br)

The rotational spectra of the complexes Ar–AgF, Ar–AgCl, and Ar–AgBr have been observed in the frequency range 6–20 GHz using a pulsed jet cavity Fourier transform microwave spectrometer. All the complexes are linear and rather rigid in the ground vibrational state, with the Ar–Ag stretching frequency estimated as ∼140 cm−1. Isotopic data have been used to calculate an r0 structure for Ar–AgF, while for Ar–AgCl and Ar–AgBr partial substitution structures have also been obtained. To reduce zero-point vibrational effects a double substitution method (rd) was employed to calculate the structures of Ar–AgCl and Ar–AgBr. The Ar–Ag bond distance has been found to be rather short and to range from 2.56 Å in Ar–AgF to 2.64 Å in Ar–AgBr. Ab initio MP2 and density functional theory calculations for Ar–AgF and Ar–AgCl model the geometries and stretching frequency well, and predict an Ar–Ag bond energy in Ar–AgF of ∼23 kJ mol−1. These results indicate that the Ar–AgX complexes are more strongly bound than typical van der Waals complexes. Analysis of the halogen nuclear quadrupole coupling constants was unable to confirm whether extensive electron rearrangement occurs upon formation of the complexes.

Behaviors of an excess proton in solute-containing water clusters: A case study of H+(CH3OH)(H2O)1–6

Behaviors of an excess proton in solute-containing water clusters were investigated using infrared spectroscopy and ab initio calculations. This investigation characterized the structures of protonated methanol-water clusters, H+(CH3OH)(H2O)n with n=2–6, according to their nonhydrogen-bonded and hydrogen-bonded OH stretches in the frequency range of 2700–3900 cm−1. Ab initio calculations indicated that the excess proton in these clusters can be either localized at a site closer to methanol, forming a methyloxonium ion core (CH3OH2+), or at a site closer to water, forming a hydronium ion core (H3O+). Infrared spectroscopic measurements verified the calculations and provided compelling evidence for the coexistence of two distinct structural isomers, CH3OH2+(H2O)3 and H3O+(CH3OH)(H2O)2, in a supersonic expansion. The spectral signatures of them (either CH3OH2+ or H3O+ centered) are the free-OH stretching absorption band at 3706 cm−1 of a single-acceptor-single-donor H2O, and the band at 3673 cm−1 of a single-acceptor CH3OH. At n=4–6, the clusters adopt structures similar to their pure water analogs with five-membered rings starting to form at n=5. The position of the excess proton in them varies sensitively with the number of solvent water molecules as well as the geometry of the clusters. To further elucidate the behaviors of the excess proton in these clusters, we analyze in detail the potential energy surface along the proton transfer coordinate for two specific isomers of n=2 and 4: MW2II and MW4I. It is found that the proton can be nearly equally shared by methanol and the water dimer subunit in the form of CH3OH–H+–(H2O)2, as substantiated by hydrogen bond cooperativity and zero-point vibrational effects.

Theoretical Conformational Analysis of Thiacrown Macrocycles

A gas phase conformational analysis was performed on four sulfur-containing macrocycles (9-thiacrown-3, 12-thiacrown-4, 15-thiacrown-5, and 18-thiacrown-6) using a combination of empirical and ab initio methods. Candidates for low-lying conformers were initially generated from high-temperature molecular dynamics simulations. A more computationally manageable subset of conformations was selected for further study based on their relative energies at successively higher levels of ab initio theory. The highest level of theory included second-order perturbation theory with the aug-cc-pVDZ basis set. The lowest conformation of 9-thiacrown-3 was found to have an exodentate C2 structure with an electronic energy that is 4 kcal/mol below the C3 crystal structure. For 12-thiacrown-4, the lowest energy structure possesses D4 structure in both the gas and crystal phase. In the case of 15-thiacrown-5 the lowest energy conformer possesses an oblong, partially exodentate, gas phase structure with C2 symmetry. The crystal structure has C1 symmetry and lies 3 kcal/mol higher in energy. 18-Thiacrown-6 has an exodentate C2 symmetry, which is estimated with a large uncertainty to be 1 kcal/mol below the folded C2 structure of the crystal. Zero-point vibrational effects shift relative energies by up to 0.3 kcal/mol across an energy span of 5−7 kcal/mol, but the effect on close-lying conformers is less.

Muonium as a hydrogen analogue in silicon and germanium: Quantum effects and hyperfine parameters

We report a first-principles theoretical study of hyperfine interactions, zero-point effects, and defect energetics of muonium and hydrogen impurities in silicon and germanium. The spin-polarized density-functional method is used, with the crystalline orbitals expanded in all-electron Gaussian basis sets. The behavior of hydrogen and muonium impurities at both the tetrahedral and bond-centered sites is investigated within a supercell approximation. To describe the zero-point motion of the impurities, a double adiabatic approximation is employed in which the electron, muon/proton, and host lattice degrees of freedom are decoupled. Within this approximation the relaxation of the atoms of the host lattice may differ for the muon and proton, although in practice the difference is found to be slight. With the inclusion of zero-point motion the tetrahedral site is energetically preferred over the bond-centered site in both silicon and germanium. The hyperfine and superhyperfine parameters, calculated as averages over the motion of the muon, agree reasonably well with the available data from muon spin resonance experiments.

A new variational coupled-electron pair approach to the intermolecular interaction calculation in the framework of the valence bond theory: The case of the water dimer system

A general nonorthogonal coupled-electron pair approach based on the intermediate optimization of virtual orbitals is presented. The resulting procedure, similar to the independent electron pair approximation scheme, is developed in the framework of the valence bond (VB) theory, where the effect of the overlap is directly taken into account. Nonorthogonal virtual orbitals optimal for intermolecular correlation effects were determined starting from the self-consistent field for molecular interaction wave function. These were used in the context of a general ab initio variational multistructure VB wave function consisting of double excitations arising from simultaneous single excitations localized on each monomer. The basis set superposition error is excluded in an a priori fashion and geometry relaxation effects are naturally taken into account. As an application example, the equilibrium structure and binding energy of the water dimer system were determined. The equilibrium oxygen–oxygen distance results to be 2.954 Å, in good agreement with the experimental values (2.946 or 2.952 Å) corrected for anharmonicity of the dimer vibrations. The estimated equilibrium interaction energy is −5.02 kcal/mol, thus comparing favorably with the experimental value of −5.44±0.7 kcal/mol. Taking zero-point vibrational effects into account, the calculated binding enthalpy is −3.22 kcal/mol, in accordance with the experimental estimate of −3.59±0.5 kcal/mol, determined from measures of thermal conductivity of the vapor. The importance of employing basis sets that include diffuse polarization functions in correlated calculations on hydrogen-bonded systems is confirmed.

Quantum effects in the dissociative adsorption of hydrogen

Three-dimensional quantum and classical dynamical calculations of the dissociative adsorption of hydrogen have been performed, in which, besides one reaction path coordinate, the lateral degrees of freedom of the hydrogen center of mass were taken into account. These calculations were compared to results obtained by classical and quantum sudden approximations, which assessed the importance of tunneling, zero-point effects, and also steering in the dissociative adsorption of hydrogen. For energies below the minimum barrier height, tunneling is of course the relevant mechanism for dissociation, but above the minimum barrier height quantization and zero-point effects become more prominent. Zero-point effects suppress the dissociation probability; however, for energies slightly above the minimum barrier height, steering of the particles is only operative in the quantum dynamics and can thereby almost compensate the suppression of the quantum sticking probabilities due to zero-point effects, compared to the classical calculations. The consequences of these findings with respect to the concept of zero-point corrections in order to obtain effective quantum barrier heights are discussed. The results presented in this study should be relevant for the reaction and propagation dynamics in all systems containing hydrogen.

Towards an effective computational tool for the study of radiation-induced lesions of DNA bases: Hydrogen addition to thymine as a test case

Radiation-induced addition of a hydrogen atom to the 5,6 double bond of thymine gives rise to the 5,6-dihydro-5-thymyl or 5,6-dihydro-6-thymyl radicals. The activation and reaction energies governing these reactions were investigated by Hartree–Fock, perturbative many-body, and Kohn–Sham methods also taking the zero-point, thermal and entropic effects into account. Among the different methods, only the B3LYP approach consistently provides reliable structural, spectroscopic and energetic characteristics both for closed- and open-shell systems. At this level, formation of the 5,6-dihydro-5-thymyl radical is preferred from both thermodynamic and kinetic points of view. This is in agreement with the predominance of products derived from this radical intermediate confirmed by several experimental studies.

Large-amplitude motion in highly quantum clusters: high-resolution infrared absorption studies of jet-cooled H2–HCl and H2–DCl

High-resolution infrared spectroscopy is used to interrogate a series of inter and intramolecular vibrational quantum states in jet-cooled ortho and para H2–HCl and H2–DCl complexes, which as a result of weak binding and large zero-point effects provide a novel dynamical window into large-amplitude motion in highly quantum mechanical clusters. The fundamental vHCl=1←0 stretch bands of H2–HCl/DCl are observed and elucidate dramatic differences in the vibrationally averaged intermolecular alignment of the H2 subunit, i.e., T-shaped vs. more nearly isotropic for the lowest ortho (Π) and para (Σ) nuclear spin states, respectively. The two internal-rotor states correlating with H2(j=1) in the o-H2–HCl complex are observed via fundamental and combination band excitation built on vHCl=1←0. The 8.5 cm−1 internal-rotor splitting between the ground (Π) and excited (Σ) H2 alignments confirms the T-shaped minimum energy configuration for the intermolecular potential, with the HCl proton donating into the H2 subunit. At even higher energies for o-H2–HCl, a rich but highly perturbed spectrum of combination band transitions is observed due to the strongly Coriolis coupled manifold ((2jH2+1)(2jHCl+1)=9) of levels correlating with H2(j=1) and HCl(j=1) subunits. Rotational predissociation broadening accompanied by an abrupt cut off in these combination band spectra is observed and used to estimate a dissociation energy window of D0=45±2 and 47±2 cm−1 for the vHCl=0 and 1 intramolecular HCl stretching states, respectively, of the o-H2–HCl complex.

The inner-hydrogen migration and ground-state structure of porphycene

Following on from previous work on free-base porphyrin, we present the results of a comprehensive study on the structure and inner-hydrogen migration in porphycene, a structural isomer of porphyrin. We used density functional theory with the hybrid B3-LYP exchange-correlation functional, and both the 6-31G(d) and a triple-zeta double-polarization (TZ2P) basis set (the latter containing 726 contracted basis functions). Full geometry optimizations were carried out and all stationary points were characterized by vibrational analysis. A scaled quantum mechanical (SQM) treatment of the theoretical force constants shows convincingly that the trans-isomer is the ground state, with trans–trans inner-hydrogen migration taking place—as is the case with porphyrin—in a two-step process via a (highly unstable) cis intermediate. With the TZ2P basis, excluding zero-point effects, the trans–cis barrier height is 4.9 kcal/mol, the cis–trans energy difference is 2.4 kcal/mol and the reverse cis–trans barrier height is only 2.5 kcal/mol. We also map out and fully characterize an alternative, high-energy migration path involving a second, nonplanar cis isomer.

Ab initio MO–VB study of water dimer

The equilibrium structure and binding energy of the water dimer system were determined by employing a general ab initio VB approach. Starting from the SCF–MI wavefunction, non-orthogonal virtual orbitals optimal for intermolecular correlation terms have been determined. BSSE is excluded in an a priori fashion and geometry relaxation effects are naturally taken into account. The equilibrium geometry corresponds to R O–O=3.00 Å, β=134.5° and α=2.5°, in agreement with the experimental values. The donor OH bond results elongated by 0.002 Å. The estimated equilibrium binding energy of the water dimer is −4.69 kcal/mol. Taking zero-point vibrational effects into account, the binding enthalpy is −3.1 kcal/mol, to be compared with the experimental estimate of −3.59±0.5 kcal/mol, determined from measurements of thermal conductivity of the vapour.

Ab initioquantum and molecular dynamics of the dissociative adsorption of hydrogen on Pd(100)

The dissociative adsorption of hydrogen on Pd(100) has been studied by ab initio quantum dynamics and ab initio molecular dynamics calculations. Treating all hydrogen degrees of freedom as dynamical coordinates implies a high dimensionality and requires statistical averages over thousands of trajectories. An efficient and accurate treatment of such extensive statistics is achieved in two steps: In a first step we evaluate the ab initio potential energy surface (PES) and determine an analytical representation. Then, in an independent second step dynamical calculations are performed on the analytical representation of the PES. Thus the dissociation dynamics is investigated without any crucial assumption except for the Born-Oppenheimer approximation which is anyhow employed when density-functional theory calculations are performed. The ab initio molecular dynamics is compared to detailed quantum dynamical calculations on exactly the same ab initio PES. The occurence of quantum oscillations in the sticking probability as a function of kinetic energy is addressed. They turn out to be very sensitive to the symmetry of the initial conditions. At low kinetic energies sticking is dominated by the steering effect which is illustrated using classical trajectories. The steering effects depends on the kinetic energy, but not on the mass of the molecules. Zero-point effects lead to strong differences between quantum and classical calculations of the sticking probability. The dependence of the sticking probability on the angle of incidence is analysed; it is found to be in good agreement with experimental data. The results show that the determination of the potential energy surface combined with high-dimensional dynamical calculations, in which all relevant degrees of freedon are taken into account, leads to a detailed understanding of the dissociation dynamics of hydrogen at a transition metal surface.