Mean Unsigned Deviation Research Articles

Explicitly correlated composite thermochemistry of transition metal species

Atomization energies were calculated using explicitly correlated coupled cluster methods with correlation consistent basis sets for a series of 19 small molecules containing 3d transition metal atoms. The atomization energies were calculated using a modified Feller-Peterson-Dixon approach in which CCSD(T) complete basis set (CBS) limits were obtained using extrapolations of aVTZ∕aVQZ CCSD(T)-F12b correlation energies, and then a series of additive contributions for relativity, core correlation, higher order correlation, and zero-point vibrations were included. The frozen-core CBS limits calculated with F12 methods closely matched the more computational expensive conventional awCVQZ∕awCV5Z CBS extrapolations, with a mean unsigned deviation of just 0.1 kcal∕mol. In particular, the CCSD(T∗)-F12b∕aVDZ and aVTZ atomization energies were more accurate on average than the conventional CCSD(T)∕aVQZ and aV5Z results, respectively. In several cases the effects of higher order correlation beyond CCSD(T), as judged by CCSDT and CCSDT(Q)Λ calculations, were greater than 1 kcal∕mol, reaching 4.5 kcal∕mol for CrO3. For the 16 molecules of this study with experimental uncertainties of ∼3.5 kcal∕mol or less, the final composite heats of formation have a mean unsigned deviation (MUD) from experiment of just 1.3 kcal∕mol, which is slightly smaller than the average of the experimental uncertainties, 1.8 kcal∕mol. The root mean square deviation (RMS) is only slightly larger at 1.7 kcal∕mol. Without the contributions due to higher order correlation effects, the MUD and RMS rise to 2.1 and 2.8 kcal∕mol, respectively. To facilitate the F12 calculations, new (aug-)cc-pVnZ∕MP2Fit (n = Q, 5) and (aug-)cc-pwCVTZ∕MP2Fit auxiliary basis sets were also developed for the transition metal atoms.

Assessment of n-Electron Valence State Perturbation Theory for Vertical Excitation Energies.

The multireference n-electron Valence State Perturbation Theory is applied to a benchmark set of 28 organic molecules compiled by Schreiber et al. J. Chem. Phys. (2008) 128, 13. Different types of low-lying vertical excitation energies are computed using the same geometries and TZVP basis set as in the original work. The previously published coupled cluster CC3 results are used as a reference. The complete active space second order perturbation theory (CASPT2) results, as well as the results of second order N-electron valence perturbation theory (NEVPT2) (both in their single-state variants) are evaluated against this reference set, which includes 153 singlet and 72 triplet vertical transition energies. NEVPT2 calculations are carried out in two variants: the partially contracted (PC) and the strongly contracted (SC) scheme. The statistical evaluation with respect to CC3 is found to be similar for both: the mean unsigned deviations is 0.28 eV for singlets and 0.16 eV for triplets for PC-NEVPT2, while it is 0.23 and 0.17 eV for SC-NEVPT2, respectively. Further analysis has shown that deficiencies in the zeroth-order wave functions, in particular for the subset of π → π* singlet excitations, are responsible for the largest deviations from CC3. Those states have either a charge transfer or an ionic character. For the remaining singlet and all triplet excitations the general trend was established that NEVPT2 tends to slightly overestimate excitation energies while CASPT2 slightly underestimates them. However, overall, both methods are of very similar accuracy provided that the IPEA shift is used in the CASPT2 method. Interestingly, the conclusions reached in this study are independent of the orbital canonicalization scheme used in the NEVPT2 calculation.

Evolution of Structure–Reactivity Correlations for the Hydrogen Abstraction Reaction by Hydroxyl Radical and Comparison with That by Chlorine Atom

A structure-reactivity correlation for the reaction (HO(•) + HCR3 → HOH + CR3(•)) has been formulated: log k298(per H, cm(3)/molecule·s) = -0.000630ΔrH(2) - 0.151ΔrH - 1.056∑F - 1.053∑R - 21.26 (r(2) = 0.885; n = 70; mean unsigned deviation = 0.29 log units), where ΔrH is the reaction enthalpy (kJ/mol) and F and R represent the dissection of Hammett's σpara constant into its field/inductive and resonance effects, and compared for the analogous case for Cl(•) (ref 1). Although more exothermic, the dependence of HO(•) on ΔrH is somewhat greater than Cl(•). However the dependence on F and R is much less, suggestive of less charge separation in the transition state for the less electronegative HO(•). The range of k(OH) is significantly less than that of Cl(•), i.e., it is less dependent on substrate structure. Yet a crossover exists such that k(Cl) > k(HO) predominates for more reactive cases whereas k(Cl) < k(OH) characterizes the less reactive. The Arrhenius parameters reveal that this crossover results from a change in {E(Cl) - E(OH)} from negative to positive. In contrast, whereas the A factors for both increase significantly as reactivity increases, {A(Cl)/A(OH)} always exceeds unity.

Assessing the Accuracy of Inhomogeneous Fluid Solvation Theory in Predicting Hydration Free Energies of Simple Solutes

Accurate prediction of hydration free energies is a key objective of any free energy method that is applied to modeling and understanding interactions in the aqueous phase. Inhomogeneous fluid solvation theory (IFST) is a statistical mechanical method for calculating solvation free energies by quantifying the effect of a solute acting as a perturbation to bulk water. IFST has found wide application in understanding hydration phenomena in biological systems, but quantitative applications have not been comprehensively assessed. In this study, we report the hydration free energies of six simple solutes calculated using IFST and independently using free energy perturbation (FEP). This facilitates a validation of IFST that is independent of the accuracy of the force field. The results demonstrate that IFST shows good agreement with FEP, with an R2 coefficient of determination of 0.99 and a mean unsigned difference of 0.7 kcal/mol. However, sampling is a major issue that plagues IFST calculations and the results suggest that a histogram method may require prohibitively long simulations to achieve convergence of the entropies, for bin sizes which effectively capture the underlying probability distributions. Results also highlight the sensitivity of IFST to the reference interaction energy of a water molecule in bulk, with a difference of 0.01 kcal/mol changing the predicted hydration free energies by approximately 2.4 kcal/mol for the systems studied here. One of the major advantages of IFST over perturbation methods such as FEP is that the systems are spatially decomposed to consider the contribution of specific regions to the total solvation free energies. Visualizing these contributions can yield detailed insights into solvation thermodynamics. An insight from this work is the identification and explanation of regions with unfavorable free energy density relative to bulk water. These regions contribute unfavorably to the hydration free energy. Further work is necessary before IFST can be extended to yield accurate predictions of binding free energies, but the work presented here demonstrates its potential.

Vibrational Configuration Interaction Using a Tiered Multimode Scheme and Tests of Approximate Treatments of Vibrational Angular Momentum Coupling: A Case Study for Methane

We present vibrational configuration interaction calculations employing the Watson Hamiltonian and a multimode expansion. Results for the lowest 36 eigenvalues of the zero total angular momentum rovibrational spectrum of methane agree with the accurate benchmarks of Wang and Carrington to within a mean unsigned deviation of 0.68, 0.033, and 0.014 cm(-1) for 4-mode, 5-mode, and 6-mode representations, respectively. We note that in the case of the 5-mode results, this is a factor of 10 better agreement than for 5-mode calculations reported earlier by Wu, Huang, Carter, and Bowman for the same set of eigenvalues, which indicates that the multimode expansion is even more rapidly convergent than previously demonstrated. Our largest calculations employ a tiered approach with matrix elements treated using a variable-order multimode expansion with orders ranging from 4-mode to 7-mode; strategies for assigning matrix elements to particular multimode tiers are discussed. Improvements of 7-mode coupling over 6-mode coupling are small (averaging 0.002 cm(-1) for the first 36 eigenvalues) suggesting that 7-mode coupling is sufficient to fully converge the results. A number of approximate treatments of the computationally expensive vibrational angular momentum terms are explored. The use of optimized vibrational quadratures allows rapid integration of the matrix elements, especially the vibrational angular momentum terms, which require significantly fewer quadrature points than are required to integrate the potential. We assign the lowest 243 states and compare our results to those of Wang and Carrington, who provided assignments for the same set of states. Excellent agreement is observed for most states, but our results are lower for some of the higher-energy states by as much as 20 cm(-1), with the largest deviations being for the states with six quanta of excitation in the F2 bends, suggesting that the earlier results were not fully converged with respect to the basis set. We also provide corrections to several of the state assignments published previously.

Anharmonic zero point vibrational energies: Tipping the scales in accurate thermochemistry calculations?

Anharmonic zero point vibrational energies (ZPVEs) calculated using both conventional CCSD(T) and MP2 in combination with vibrational second-order perturbation theory (VPT2) are compared to explicitly correlated CCSD(T)-F12 and MP2-F12 results that utilize vibrational configuration interaction (VCI) theory for 26 molecules of varying size. Sequences of correlation consistent basis sets are used throughout. It is found that the explicitly correlated methods yield results close to the basis set limit even with double-zeta quality basis sets. In particular, the anharmonic contributions to the ZPVE are accurately recovered at just the MP2 (or MP2-F12) level of theory. Somewhat surprisingly, the best vibrational CI results agreed with the VPT2 values with a mean unsigned deviation of just 0.09 kJ/mol and a standard deviation of just 0.11 kJ/mol. The largest difference was observed for C(4)H(4)O (0.34 kJ/mol). A simplified version of the vibrational CI procedure that limited the modal expansion to at most 2-mode coupling yielded anharmonic corrections generally within about 0.1 kJ/mol of the full 3- or 4-mode results, except in the cases of C(3)H(8) and C(4)H(4)O where the contributions were underestimated by 1.3 and 0.8 kJ/mol, respectively (34% and 40%, respectively). For the molecules considered in this work, accurate anharmonic ZPVEs are most economically obtained by combining CCSD(T)-F12a/cc-pVDZ-F12 harmonic frequencies with either MP2/aug-cc-pVTZ/VPT2 or MP2-F12/cc-pVDZ-F12/VCI anharmonic corrections.

Evolution of Structure–Reactivity Correlations for the Hydrogen Abstraction Reaction by Chlorine Atom

Empirical structure-reactivity correlations are developed for log k(298), the gas-phase rate constants for the reaction (Cl(•) + HCR(3) → ClH + CR(3)(•)). It has long been recognized that correlation with Δ(r)H is weak. The poor performance of the linear Evans-Polanyi formulation is illustrated and was little improved by adding a quadratic term, for example, by making its slope smoothly dependent on Δ(r)H [η ≡ (Δ(r)H - Δ(r)H(min))/(Δ(r)H(max) - Δ(r)H(min))]. The "polar effect" ((δ-)Cl---H---CR(3)(δ+))(++) has also been long discussed, but there is no formalization of this dependence based on widely available independent variable(s). Using the sum of Hammett constants for the R substituents also gave at best modest correlations, either for σ(para) or for its dissection into F (field/inductive) and R (resonance) effects. Much greater success was achieved by combining these approaches with the preferred independent variable set being either [(Δ(r)H)(2), Δ(r)H, ΣF, and ΣR] or [η, Δ(r)H, ΣF, and ΣR]. For 64 rate constants that span 7 orders of magnitude, these correlation formulations give r(2) > 0.87 and a mean unsigned deviation of <0.5 log k units, with even better performance if primary, secondary, and tertiary reaction centers are treated separately.

How Accurate Can a Local Coupled Cluster Approach Be in Computing the Activation Energies of Late-Transition-Metal-Catalyzed Reactions with Au, Pt, and Ir?

To improve the accuracy of local coupled cluster (LCC) methods in computing activation energies, we propose herein a new computational scheme. Its applications to various types of late-transition-metal-catalyzed reactions involving Au, Pt, and Ir indicate that the new corrective approach for LCC methods can downsize the mean unsigned deviation and maximum deviation, from the CCSD(T)/CBS reference, to about 0.3 and 0.9 kcal/mol. Using this method, we also calibrated the performance of popular density functionals, with respect to the same test set of reactions. It is concluded that the best functional is the general-purpose double hybrid functional B2GP-PLYP. Other well-performing functionals include the "kinetic" functionals M06-2X and BMK, which have a large percentage of HF exchange, and general-purpose functionals like PBE0 and wB97X. Comparatively, general-purpose functionals like PBE0 and TPSSh perform much better than the tested "kinetic" functionals for Pt-/Ir-catalyzed reactions, while the opposite is true for Au-catalyzed reactions. In contrast, wB97X performs more uniformly in these two classes of reactions. These findings hint that even within the scope of late transition metals, different types of reactions may require different types of optimal DFT methods. Empirical dispersion correction of DFT was found to have a small or no effect on the studied reactions barriers.

Molecular Modeling and Simulation of Vapor–Liquid Equilibria of Ethylene Oxide, Ethylene Glycol, and Water as Well as their Binary Mixtures

Mixtures containing ethylene oxide are technically highly relevant but hazardous so that typically only few reliable experimental data are available. They are therefore interesting candidates for the application of molecular modeling and simulation to predict thermodynamic properties. The industrially most important ethylene oxide containing mixtures are those with water and ethylene glycol. An excellent molecular model for ethylene oxide is available from prior work. Because the molecular models for water from the literature do not yield satisfactory results for the vapor–liquid equilibrium over a wide temperature range, a new water model is developed. Furthermore, also a new molecular model for ethylene glycol is developed. The models for ethylene glycol and water show mean unsigned deviations with respect to experimental data, considering the whole temperature range from triple point to critical point, of 0.8 and 1.1% for the saturated liquid density, 4.8 and 7.2% for the vapor pressure, and 13.4 and 2.8% for the enthalpy of vaporization, respectively. Vapor–liquid equilibria of all three binary mixtures are determined by molecular simulation, and in general, a good agreement is found with the available experimental data. The models can be used for subsequent predictions at other conditions.

Review of Rate Constants and Exploration of Correlations of the Halogen Transfer Reaction of Trisubstituted Carbon-Centered Radicals with Molecular Halogens

Rate constants for the reaction (R'(3)C(•) + X(2) → R'(3)CX + X(•); X = F, Cl, Br, I) are reviewed. Because of curved Arrhenius plots and negative E(X) values, empirical structure-reactivity correlations are sought for log k(X,298) rather than E(X). The well-known poor correlation with measures of reaction enthalpy is demonstrated. The best quantitative predictor for R'(3)C(•) is Σσ(p), the sum of the Hammett σ(p) constants for the three substituents, R'. Electronegative substituents with lone pairs, such as halogen and oxygen, thus appear to destabilize the formation of a polarized prereaction complex and/or TS ((δ+)R- - -X- - -X(δ-)) by σ inductive/field electron withdrawal while simultaneously stabilizing them by π resonance electron donation. The best quantitative predictor of the reactivity order of the halogens, I(2) > Br(2) ≫ Cl(2) ≈ F(2), is the polarizability of the halogen, α(X(2)). For the data set of 60 rate constants which span 6.5 orders of magnitude, a modestly successful correlation of log k(X,298) is achieved with only two parameters, Σσ(p) and α(X(2)), with a mean unsigned deviation of 0.59 log unit. How much of this residual variance is the result of inaccuracies in the data in comparison with oversimplification of the correlation approach remains to be seen.

Molecular simulation study on the solubility of carbon dioxide in mixtures of cyclohexane + cyclohexanone

Molecular simulation data on the vapor–liquid equilibrium and the Henry's law constant of carbon dioxide in mixtures of cyclohexane + cyclohexanone are presented. The agreement between simulation results and the available experimental data is good. For the present predictions, new molecular models for cyclohexane and cyclohexanone are developed. The resulting molecular models for cyclohexane and cyclohexanone show mean unsigned deviations with respect to experimental data considering the whole temperature range from triple point to critical point of 0.4% and 0.9% for the saturated liquid density, 3% and 2.7% for the vapor pressure, and 6% and 5.3% for the enthalpy of vaporization, respectively. The carbon dioxide model is taken from preceding work.

Use of Solution-Phase Vibrational Frequencies in Continuum Models for the Free Energy of Solvation

We find that vibrational contributions to a solute's free energy are in general insensitive to whether the solute vibrational frequencies are computed in the gas phase or in solution. In most cases, the difference is smaller than the intrinsic error in solvation free energies associated with the continuum approximation to solvation modeling, although care must be taken to avoid spurious results associated with limitations in the quantum-mechanical harmonic-oscillator approximation for very low-frequency molecular vibrations. We compute solute vibrational partition functions in aqueous and carbon tetrachloride solution and compare them to gas-phase molecular partition functions computed with the same level of theory and the same quasiharmonic approximation for the diverse and extensive set of molecules and ions included in the training set of the SMD continuum solvation model, and we find mean unsigned differences in vibrational contributions to the solute free energy of only about 0.2 kcal/mol. On the basis of these results and a review of the theory, we conclude, in contrast to previous work (Ho, J.; Klamt, H.; Coote, M. L. J. Phys. Chem. A 2010, 114, 13442), that using partition functions computed for molecules optimized in solution is a correct and useful approach for averaging over solute degrees of freedom when computing free energies of solutes in solution, and it is moreover recommended for cases where liquid and gas-phase solute structures differ appreciably or when stationary points present in liquid solution do not exist in the gas phase, for which we provide some examples. When gas-phase and solution-phase geometries and frequencies are similar, the use of gas-phase geometries and frequencies is a useful approximation.

Automated 3-D method for the correction of axial artifacts in spectral-domain optical coherence tomography images

The 3-D spectral-domain optical coherence tomography (SD-OCT) images of the retina often do not reflect the true shape of the retina and are distorted differently along the x and y axes. In this paper, we propose a novel technique that uses thin-plate splines in two stages to estimate and correct the distinct axial artifacts in SD-OCT images. The method was quantitatively validated using nine pairs of OCT scans obtained with orthogonal fast-scanning axes, where a segmented surface was compared after both datasets had been corrected. The mean unsigned difference computed between the locations of this artifact-corrected surface after the single-spline and dual-spline correction was 23.36 ± 4.04 μm and 5.94 ± 1.09 μm, respectively, and showed a significant difference (p < 0.001 from two-tailed paired t-test). The method was also validated using depth maps constructed from stereo fundus photographs of the optic nerve head, which were compared to the flattened top surface from the OCT datasets. Significant differences (p < 0.001) were noted between the artifact-corrected datasets and the original datasets, where the mean unsigned differences computed over 30 optic-nerve-head-centered scans (in normalized units) were 0.134 ± 0.035 and 0.302 ± 0.134, respectively.

Universal Method to Calculate the Stability, Electronegativity, and Hardness of Dianions

The electronic stability of gas-phase dianions of arbitrary size, X(2-), is determined by the first universal method to calculate second electron affinities, A(2). The model expresses A(2,calc) = A(1) - (7/6)η(0) by the first electron affinity, A(1), and chemical hardness, η(0), of the neutral "grandparent" species. A comparison with 37 reference data of atoms, molecules, superatoms, and clusters yields A(2,ref) = 1.004A(2,calc) - 0.023 eV, with a mean unsigned deviation of MUD = 0.095 eV and a correlation coefficient of R = 0.9987. Predictions of second electron affinities are given for a further 24 species. The universality of the model is apparent from the broad variety of compounds formed by 30 diverse elements. The electronegativity and hardness of dianions are determined for the first time as χ(X(2-)) = A(2) and η(X(2-)) = (7/12)η(0), respectively. Pearson and Parr's operational assumption regarding the hardness of anionic bases for the hard-soft acid-base (HSAB) principle is rationalized, and predictions for hard and soft dianionic bases are presented. For trianions, first criteria and predictions for electronic stability are given and require A(1) > (7/4)η(0).

Assessment of Gaussian-4 theory for energy barriers

Gaussian-4 (G4) theory, and various modifications, are assessed for the calculation of the heights of reaction energy barriers. The results indicate that G4 theory based on QCISD/MG3 geometries shows good accuracy for the calculation of bond-making and bond-breaking reaction barriers with a mean unsigned deviation of 0.71 kcal/mol for 76 barrier heights involving both hydrogen and non-hydrogen transfer reactions. G4 theory based on B3LYP/6-31G(2df,p) geometries has a larger mean unsigned deviation of 1.36 kcal/mol for the 76 barriers heights due to deficiencies in the geometries of transition states for fluorine-containing systems.

Molecular model for carbon dioxide optimized to vapor-liquid equilibria

A molecular model for carbon dioxide is presented, and the parameters of the Lennard-Jones sites, the bond length, and the quadrupole moment are optimized to experimental vapor-liquid equilibrium data. The resulting molecular model shows mean unsigned deviations to the experiment over the whole temperature range from triple point to critical point of 0.4% in saturated liquid density, 1.8% in vapor pressure, and 8.1% in enthalpy of vaporization. The molecular model is assessed by comparing predicted thermophysical properties with experimental data and a reference equation of state for a large part of the fluid region. The average deviations for density and residual enthalpy are 4.5% and 1.7%, respectively. The model is also capable to predict the radial distribution function, the second virial coefficient, and transport properties, the average deviations of the latter are 12%.

Flexible-boundary QM/MM calculations: II. Partial charge transfer across the QM/MM boundary that passes through a covalent bond

Recently, based on the principle of electronic chemical potential equalization and the principle of charge conservation, we proposed a flexible-boundary scheme that allows both partial charge transfer and self-consistent polarization between the quantum mechanical (QM) and molecular mechanical (MM) subsystems in QM/MM calculations; the scheme was applied to study the atomic charges in selected ion–solvent complexes. In the present contribution, we further extend the flexible-boundary treatment to handle the QM/MM boundary passing through covalent bonds. We find that the flexible-boundary redistributed charge and dipole schemes yield reasonable agreement with full-QM calculations for a number of molecular ions and amino acids with charged side chains. Using the full-QM results as reference, the mean unsigned deviations are computed to be 0.06 e for atomic partial charges of the QM atoms, 0.11 e for the amounts of charge transfer between the QM and MM subsystems, and 0.016 A for the lengths of the covalent bonds that directly connect the QM and MM subsystems. The results indicate the importance of accounting for partial charge transfer across the QM/MM boundary when the QM subsystems are charged.

How accurate are continuum solvation models for drug-like molecules?

We have estimated the hydration free energy for 20 neutral drug-like molecules, as well as for three series of 6-11 inhibitors to avidin, factor Xa, and galectin-3 with four different continuum solvent approaches (the polarised continuum method the Langevin dipole method, the finite-difference solution of the Poisson equation, and the generalised Born method), and several variants of each, giving in total 24 different methods. All four types of methods have been thoroughly calibrated for a number of experimentally known small organic molecules with a mean absolute deviation (MAD) of 1-6 kJ/mol for neutral molecules and 4-30 kJ/mol for ions. However, for the drug-like molecules, the accuracy seems to be appreciably worse. The reason for this is that drug-like molecules are more polar than small organic molecules and that the uncertainty of the methods is proportional to the size of the solvation energy. Therefore, the accuracy of continuum solvation methods should be discussed in relative, rather than absolute, terms. In fact, the mean unsigned relative deviations of the best solvation methods, 0.09 for neutral and 0.05 for ionic molecules, correspond to 2-20 kJ/mol absolute error for the drug-like molecules in this investigation, or 2-3,000 in terms of binding constants. Fortunately, the accuracy of all methods can be improved if only relative energies within a series of inhibitors are considered, especially if all of them have the same net charge. Then, all except two methods give MADs of 2-5 kJ/mol (corresponding to an uncertainty of a factor of 2-7 in the binding constant). Interestingly, the generalised Born methods typically give better results than the Poison-Boltzmann methods.

Ab Initio Wavenumber Accurate Spectroscopy: 1CH2 and HCN Vibrational Levels on Automatically Generated IMLS Potential Energy Surfaces

We report here calculated J = 0 vibrational frequencies for (1)CH(2) and HCN with root-mean-square error relative to available measurements of 2.0 cm(-1) and 3.2 cm(-1), respectively. These results are obtained with DVR calculations with a dense grid on ab initio potential energy surfaces (PESs). The ab initio electronic structure calculations employed are Davidson-corrected MRCI calculations with double-, triple-, and quadruple-zeta basis sets extrapolated to the complete basis set (CBS) limit. In the (1)CH(2) case, Full CI tests of the Davidson correction at small basis set levels lead to a scaling of the correction with the bend angle that can be profitably applied at the CBS limit. Core-valence corrections are added derived from CCSD(T) calculations with and without frozen cores. Relativistic and non-Born-Oppenheimer corrections are available for HCN and were applied. CBS limit CCSD(T) and CASPT2 calculations with the same basis sets were also tried for HCN. The CCSD(T) results are noticeably less accurate than the MRCI results while the CASPT2 results are much poorer. The PESs were generated automatically using the local interpolative moving least-squares method (L-IMLS). A general triatomic code is described where the L-IMLS method is interfaced with several common electronic structure packages. All PESs were computed with this code running in parallel on eight processors. The L-IMLS method provides global and local fitting error measures important in automatically growing the PES from initial ab initio seed points. The reliability of this approach was tested for (1)CH(2) by comparing DVR-calculated vibrational levels on an L-IMLS ab initio surface with levels generated by an explicit ab initio calculation at each DVR grid point. For all levels ( approximately 200) below 20 000 cm(-1), the mean unsigned difference between the levels of these two calculations was 0.1 cm(-1), consistent with the L-IMLS estimated mean unsigned fitting error of 0.3 cm(-1). All L-IMLS PESs used in this work have comparable mean unsigned fitting errors, implying that fitting errors have a negligible role in the final errors of the computed vibrational levels with experiment. Less than 500 ab initio calculations of the energy and gradients are required to achieve this level of accuracy.

Atom-Based Thermochemistry: Predictions of the Sublimation Enthalpies of Group 12 Chalcogenides and the Formation Enthalpies of their Polonides

Surprising and useful linear relationships between the atomization enthalpies of molecules and the cohesion enthalpies of crystals are found by shifting the thermochemical reference zero from elements to free atoms. Although the reference shift looks extremely simple, such atom-based thermochemistry (ABT) offers a direct way to calculate and predict the standard atomization enthalpy of molecules, Delta(at) H degrees(g), or solids, Delta(at) H degrees(s), with good accuracy (J. Am. Chem. Soc. 2008, 130, 5962-5973). It appears that referencing to atoms is able to provide a new unifying perspective. For group 12 metal chalcogenides, ME with M = Zn, Cd, Hg, E = O, S, Se, Te, Po, diabatic bond dissociation enthalpies, Dd298, with reference to the 1D2 state of the chalcogen atoms are mandated, in order to analyze the bond strengths properly (Mol. Phys. 2007, 105, 1139-1155). In this case, ABT implies a 2-fold reference shift (i) from formation enthalpies to atomization enthalpies and (ii) from standard atomization enthalpies to diabatic atomization enthalpies. An excellent linear relationship is found between the Dd298(ME) values and the corresponding diabatic atomization enthalpy of the solids, Delta(at) Hd(ME, s). The regression line is Delta(at) Hd(ME, s, calc) = 2.2717Dd298(ME) + 148.1 kJ mol-1 with the correlation coefficient R = 0.9996, the standard deviation (SD) = 4.2 kJ mol-1 and a mean unsigned deviation (MAD) = 3.7 kJ mol-1. Updated and corrected gas phase standard enthalpies of formation, Delta(f) H degrees(g), are presented for all 15 group 12 metal chalcogenides, and their lack of correlation with the formation enthalpies of the crystals, Delta(f) H degrees(s), is documented. The standard sublimation enthalpies, Delta(subl) H degrees, are reported for the first time. Recent accurate theoretical Dd298 values for the group 12 metal polonides, MPo, are taken to derive the first prediction for the standard atomization, formation, and sublimation enthalpies of their solids.