A Density Functional Theory Study on the Effect of Zero‐Point Energy Corrections on the Methanation Profile on Fe(100)

The thermodynamics and kinetics of the surface hydrogenation of adsorbed atomic carbon to methane, following the reaction sequence C+4 H?CH+3 H?CH₂+2 H?CH₃+H?CH₄, are studied on Fe(100) by means of density functional theory. An assessment is made on whether the adsorption energies and overall energy profile are affected when zero‐point energy (ZPE) corrections are included. The C, CH and CH₂ species are most stable at the fourfold hollow site, while CH₃ prefers the twofold bridge site. Atomic hydrogen is adsorbed at both the twofold bridge and fourfold hollow sites. Methane is physisorbed on the surface and shows neither orientation nor site preference. It is easily desorbed to the gas phase once formed. The incorporation of ZPE corrections has a very slight, if any, effect on the adsorption energies and does not alter the trends with regards to the most stable adsorption sites. The successive addition of hydrogen to atomic carbon is endothermic up to the addition of the third hydrogen atom resulting in the methyl species, but exothermic in the final hydrogenation step, which leads to methane. The overall methanation reaction is endothermic when starting from atomic carbon and hydrogen on the surface. Zero‐point energy corrections are rarely provided in the literature. Since they are derived from C? H bonds with characteristic vibrations on the order of 2500–3000 cm^?1, the equivalent ZPE of 1/2 hν is on the order of 0.2–0.3 eV and its effect on adsorption energy can in principle be significant. Particularly in reactions between CH_x and H, the ZPE correction is expected to be significant, as additional C? H bonds are formed. In this instance, the methanation reaction energy of +0.77 eV increased to +1.45 eV with the inclusion of ZPE corrections, that is, less favourable. Therefore, it is crucial to include ZPE corrections when reporting reactions involving hydrogen‐containing species.     

Role of the anomeric effect in methanediamines in the gas phase and aqueous solutions

An ab initio study of methylenediamine and several methylated derivatives in the gas phase and aqueous solution was performed. The conformational preferences can be considered adequately described at the HF/6‐31G**//HF/6‐31G** level, because these results agree with those obtained using larger basis sets and including ZPE and electron correlation. The energy ordering is clearly dependent on the number and position of the methyl groups present in a molecule. For a first set of the compounds, the energies obtained were interpreted in terms of the anomeric effect because the favored conformers show two or one anti orientation between the nitrogen lone pair and the C N polar bond. Reverse anomeric effects were found for a second set of compounds. The NBO analysis was used to interpret these energetic tendencies and the rotational barrier around the N C bonds. Thus, the preference for the anti‐Lp N C N orientations is mainly due to charge delocalization, always stronger than the electrostatic and steric contributions included in the Lewis term. However, the origin for the reverse anomeric effect may be related to the steric hindrance associated with the methylation. The influence of water on the conformational preferences was evaluated by means of the PCM method. Contrary to expectation, the anomeric effect is not reduced in water, and the most stable conformers in the gas phase are maintained in solution. The electrostatic term of the free solvation energy is the main responsible of the energetic changes, and depends strongly on local solute–solvent interactions. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 135–150, 2001     

Dynamically biased statistical model for the ortho/para conversion in the H(2)+H(3) (+) → H(3) (+)+ H(2) reaction

In this work we present a dynamically biased statistical model to describe the evolution of the title reaction from statistical to a more direct mechanism, using quasi-classical trajectories (QCT). The method is based on the one previously proposed by Park and Light [J. Chem. Phys. 126, 044305 (2007)]. A recent global potential energy surface is used here to calculate the capture probabilities, instead of the long-range ion-induced dipole interactions. The dynamical constraints are introduced by considering a scrambling matrix which depends on energy and determine the probability of the identity/hop/exchange mechanisms. These probabilities are calculated using QCT. It is found that the high zero-point energy of the fragments is transferred to the rest of the degrees of freedom, what shortens the lifetime of H(5) (+) complexes and, as a consequence, the exchange mechanism is produced with lower proportion. The zero-point energy (ZPE) is not properly described in quasi-classical trajectory calculations and an approximation is done in which the initial ZPE of the reactants is reduced in QCT calculations to obtain a new ZPE-biased scrambling matrix. This reduction of the ZPE is explained by the need of correcting the pure classical level number of the H(5) (+) complex, as done in classical simulations of unimolecular processes and to get equivalent quantum and classical rate constants using Rice-Ramsperger-Kassel-Marcus theory. This matrix allows to obtain a ratio of hop/exchange mechanisms, α(T), in rather good agreement with recent experimental results by Crabtree et al. [J. Chem. Phys. 134, 194311 (2011)] at room temperature. At lower temperatures, however, the present simulations predict too high ratios because the biased scrambling matrix is not statistical enough. This demonstrates the importance of applying quantum methods to simulate this reaction at the low temperatures of astrophysical interest.     

Theoretical Study on the Cyclization Mechanism of Dipeptides

Cyclization is an important chemical reaction for the dipeptides containing N‐alkyl groups. The cyclization mechanism has been examined by theoretical calculations. Our calculation results indicate that the most favorable mechanism is the piperidine‐catalyzed stepwise mechanism, in which piperidine acts as a proton shuttle. The attack of the N‐terminal amino nitrogen at the C‐terminal carbonyl carbon along with the proton transfer is the rate‐limiting step. The effect of the alkyl substituent on the amide N on the cyclization reaction was then examined. Finally, the influence of the solvation effect, electronic effect and steric effect on the cyclization was investigated. It is found that all of these effects contribute to the cyclization.     

An ab initio interpretation in gas phase and aqueous solution of the generalized anomeric effect in R?O?CR2?NR2 (R = H,CH3)

The conformational stability of aminomethanol and its methylated derivatives has been investigated by means of ab initio methods in the gas phase and aqueous solution. Among the computational levels employed, HF/6‐31G**//HF/6‐31G** calculations correctly describe the conformational features of this series of compounds, and agree well with the results obtained using larger basis sets and including ZPE or electron correlation corrections. Calculated energies and geometries follow the known trends associated to the generalized anomeric effect. Thus, the most stable conformers exhibit preferences for the trans orientations of the Lp N C O and Lp O C N moieties. However, reverse anomeric effects are observed when a methyl group is bonded to the oxygen, because the Lp O C N unit prefers a gauche orientation (that is, trans Me O C N). The natural bond orbital (NBO) method was employed to explain the cited conformational preferences. According to the NBO results, trans arrangements are preferred because the stabilization due to charge delocalization is more important than electrostatic and steric contributions. This explanation agrees with the conclusions obtained by other independent procedures based on energy decomposition schemes. The NBO method was also used to explain the origin of the rotational barriers around the C O and C N bonds in terms of the balance between unfavorable hyperconjugation and electrostatic and steric effects. Changes in conformational stability caused by methylations in different molecular positions were also explained by the influence of the methyl groups on lone‐pair delocalization and on steric effects. Finally, the effect of solvation was studied by means of the ab initio PCM method, and the significant changes on relative energies found were analyzed. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 462–477, 2000     

Quasiclassical trajectory study of the Cl+CH4 reaction dynamics on a quadratic configuration interaction with single and double excitation interpolated potential energy surface

An ab initio interpolated potential energy surface (PES) for the Cl+CH(4) reactive system has been constructed using the interpolation method of Collins and co-workers [J. Chem. Phys. 102, 5647 (1995); 108, 8302 (1998); 111, 816 (1999); Theor. Chem. Acc. 108, 313 (2002)]. The ab initio calculations have been performed using quadratic configuration interaction with single and double excitation theory to build the PES. A simple scaling all correlation technique has been used to obtain a PES which yields a barrier height and reaction energy in good agreement with high level ab initio calculations and experimental measurements. Using these interpolated PESs, a detailed quasiclassical trajectory study of integral and differential cross sections, product rovibrational populations, and internal energy distributions has been carried out for the Cl+CH(4) and Cl+CD(4) reactions, and the theoretical results have been compared with the available experimental data. It has been shown that the calculated total reaction cross sections versus collision energy for the Cl+CH(4) and Cl+CD(4) reactions is very sensitive to the barrier height. Besides, due to the zero-point energy (ZPE) leakage of the CH(4) molecule to the reaction coordinate in the quasiclassical trajectory (QCT) calculations, the reaction threshold falls below the barrier height of the PES. The ZPE leakage leads to CH(3) and HCl coproducts with internal energy below its corresponding ZPEs. We have shown that a Gaussian binning (GB) analysis of the trajectories yields excitation functions in somehow better agreement with the experimental determinations. The HCl(v'=0) and DCl(v'=0) rotational distributions are as well very sensitive to the ZPE problem. The GB correction narrows and shifts the rotational distributions to lower values of the rotational quantum numbers. However, the present QCT rotational distributions are still hotter than the experimental distributions. In both reactions the angular distributions shift from backward peaked to sideways peaked as collision energy increases, as seen in the experiments and other theoretical calculations.     

Theoretical investigation of isotopic scrambling mechanisms in 2-chloroethyl methyl sulfide

Ab initio and semiempirical molecular orbital calculations have been applied to study the concerted and stepwise isotopic scrambling mechanisms of 2-chloroethyl methyl sulfide in the gas phase and in aqueous solution. The calculations reveal the structural details of the reactants, transition structures, and intermediates involved in this reaction and provide relative energy estimates. The concerted mechanism is found to be competitive with the stepwise mechanism in the gas phase, but the stepwise mechanism is favored in aqueous solution as no true transition structure for the concerted mechanism could be found using the solvation models. A combined approach of evaluating solvation energies with the generalized-Bom-plus-surface-tensions SM _x solvation models of Cramer and Truhlar at ab initio optimized geometries is found to deliver the best agreement with experimentally determined reaction barriers. Together with the recent experimental results of McManus and co-workers, the present study provides insights into the controlling factors involved in the elementary reaction steps of sulfur mustards and a solid foundation for investigations into more complex reactions of related compounds.     

CH3与NO在单、三态势能面上的反应机理

用从头算分了轨道法，在ＵＨＦ／６－３１Ｇ，水平上研究了ＣＨ３Ｏ与ＮＯ在单、三态势能面上的反应机理，发现该反应在两个势能面上均在两个彼此平行的反应途径，分别生产成产物ＣＨ３ＯＮ（ａ）和ＨＣＨＯ＋ＨＮＯ（ｂ），优化了四个途径的所有驻点的几何构型，用Ｍｏｒｏｋｕｍａ的数值分析方法计算了它们的内禀反应坐标（ＩＲＣ），各途径经零点能（ＺＰＥ）校正的活化位垒，单重态途径（ａ）为８６．８６ｋＪ．ｍｏｌ＾－１途径     

单嘧磺隆除草剂水解机理的理论研究

用量子化学中密度泛函B3LYP方法在6-31G*水平上, 对单嘧磺隆的水解机理进行了理论研究. 优化了反应过程中反应物、中间体、过渡态及产物的几何构型, 并对各个过渡态和中间体进行了振动分析确认其真实性. 结果表明: 在碱性条件下, 水解反应主要经历一个五元环的过渡态TS1, 该反应速控步骤的能垒为25.7 kJ/mol; 在中性条件下, 水解反应涉及到一个三元环的过渡态和两个四元环的过渡态, 反应的速控步骤为M3'＋H₂O→TS2', 能垒为236.5 kJ/mol. 从能量上看, 碱性条件更有利于水解反应的进行, 与实验结果吻合. 同时, 我们还考虑了溶剂效应对水解反应的影响.     

Ca(AlH4)2, CaAlH5, and CaH2+6LiBH4: Calculated dehydrogenation enthalpy, including zero point energy, and the structure of the phonon spectra

The dehydrogenation enthalpies of Ca(AlH(4))(2), CaAlH(5), and CaH(2)+6LiBH(4) have been calculated using density functional theory calculations at the generalized gradient approximation level. Harmonic phonon zero point energy (ZPE) corrections have been included using Parlinski's direct method. The dehydrogenation of Ca(AlH(4))(2) is exothermic, indicating a metastable hydride. Calculations for CaAlH(5) including ZPE effects indicate that it is not stable enough for a hydrogen storage system operating near ambient conditions. The destabilized combination of LiBH(4) with CaH(2) is a promising system after ZPE-corrected enthalpy calculations. The calculations confirm that including ZPE effects in the harmonic approximation for the dehydrogenation of Ca(AlH(4))(2), CaAlH(5), and CaH(2)+6LiBH(4) has a significant effect on the calculated reaction enthalpy. The contribution of ZPE to the dehydrogenation enthalpies of Ca(AlH(4))(2) and CaAlH(5) calculated by the direct method phonon analysis was compared to that calculated by the frozen-phonon method. The crystal structure of CaAlH(5) is presented in the more useful standard setting of P2(1)c symmetry and the phonon density of states of CaAlH(5), significantly different to other common complex metal hydrides, is rationalized.     

亚硝基苯与甲醛的反应机理和溶剂效应的理论研究

采用密度泛函理论方法RB3LYP/6-311＋＋G(d,p)研究了亚硝基苯与甲醛在单重态势能面上分别在气相和溶剂中的反应机理. 找到两条反应通道: 协同机理和分步机理, 均生成实验产物N-苯基氧肟酸C6H5NOHCHO. 计算结果表明: 亚硝基苯与甲醛在气相中分步机理为主要通道. 采用导电极化连续介质模型研究了反应体系在水、乙醇、乙腈、二氯甲烷、四氢呋喃、环己烷溶液中反应的溶剂化效应, 这些溶剂可降低反应的活化能, 但反应对溶剂的极性不敏感. 无论在气相还是溶剂中, 亚硝基苯与甲醛的分步机理为优势通道.     

O~3＋NH→HNO＋O~2反应机理的量子化学研究

用密度泛函(DFT)的B3LYP方法(6－31++G^*^*)研究了臭氧与NH自由基反应的微观机理,优化得到反应途径上的反应物,过渡态,中间体和产物的构型,通过振动分析对过渡态和中间体进行了确认。对单点用QCISD(T)/6－31++G^*^*方法计算能量,同时进行零点能校正。研究结果表明：NH与O~3反应有两条不同的反应通道,且均表现为亲电反应特征,两条不同的反应均为强放热反应。     

Theoretical studies on the conformation of saccharides

The stereochemistry of d-glucopyranose has been studied theoretically in 11 solvents. The stability of the individual conformers in solution has been compared using a method in which the total energy is divided into the energy of an isolated molecule and the solvation energy. The structure and the energy of the isolated molecule have been estimated by geometry optimization using the PCILO quantum chemical method. The solvation energy consists of electrostatic, dispersion, and cavity terms which have been determined from calculated properties of the solute and physiochemical properties of the solvents. The influence of the solvent on rotation of the individual pendant groups and the stability of anomers have been investigated. The calculated composition of the anomeric mixture of d-glucopyranose in various solvents at 25°C (e.g., in pyridine 49% is -anomer, in dimethyl sulfoxide 46%, and in water 32%) is in good agreement with the available experimental data and clearly demonstrates that the solvation properties of - and -d-glucopyranose differ. Based on the calculated abundances of anomers the magnitude of the anomeric effect has been estimated and compared with the results of corresponding calculations on other compounds.     

On the contribution of vibrational anharmonicity to the binding energies of water clusters

The second-order vibrational perturbation theory method has been used together with the B3LYP and MP2 electronic structure methods to investigate the effects of anharmonicity on the vibrational zero-point energy (ZPE) contributions to the binding energies of (H2O)n, n = 2-6, clusters. For the low-lying isomers of (H2O)6, the anharmonicity correction to the binding energy is calculated to range from -248 to -355 cm(-1). It is also demonstrated that although high-order electron correlation effects are important for the individual vibrational frequencies, they are relatively unimportant for the net ZPE contributions to the binding energies of water clusters.     

Development of a finite-temperature density functional approach to electrochemical reactions

We present a computational method to calculate the electronic states of a molecule in an electrochemical environment. The method is based on our recently developed finite-temperature density functional theory approach to calculate the electronic structures at a constant chemical potential. A solvent effect is treated at the level of the extended self-consistent reaction field model, which allows considering a nonequilibrium solvation effect. An exchange-correlation functional with a long-range correction is employed in this calculation, because the functional is adjusted so that the derivative discontinuity of energy with respect to a number of electrons could be satisfied. It has been found that the derivative discontinuity condition plays a crucial role in an electrochemical system. The computational results are presented for a reaction of NO(+) + e(-) <==> NO in chemical equilibrium. Owing to the improvement in the solvation effect and the exchange-correlation functional, the calculated activation free energy is in good agreement with experimental results.     

Computational Analysis of Solute–Solvent Coupling Magnitude in the Z/E Isomerization Reaction of Nitroazobenzene and Benzylideneanilines

The dynamic solvent effect often arises in solution reactions, where coupling between chemical reaction and solvent fluctuation plays a decisive role in the reaction kinetics. In this study, the Z/E isomerization reaction of nitoroazobenzene and benzylideneanilines in the ground state was computationally studied by molecular dynamics simulations. The non-equilibrium solvation effect was analyzed using two approaches: (1) metadynamics Gibbs energy surface exploration and (2) solvation Gibbs energy evaluation using a frozen solvation droplet model. The solute–solvent coupling parameter (C_coupled) was estimated by the ratio of the solvent fluctuation Gibbs energy over the corresponding isomerization activation Gibbs energy. The results were discussed in comparison with the ones estimated by means of the analytical models based on a reaction–diffusion equation with a sink term. The second approach using a frozen solvation droplet reached qualitative agreement with the analytical models, while the first metadynamics approach failed. This is because the second approach explicitly considers the non-equilibrium solvation in the droplet, which consists of a solute at the reactant geometry immersed in the pre-organized solvents fitted with the solute at the transition state geometry.     

Mixed quantum/classical investigation of the photodissociation of NH3(A) and a practical method for maintaining zero-point energy in classical trajectories

The photodissociation dynamics of ammonia upon excitation of the out-of-plane bending mode (mode nu(2) with n(2)=0,[ellipsis (horizontal)],6 quanta of vibration) in the A electronic state is investigated by means of several mixed quantum/classical methods, and the calculated final-state properties are compared to experiments. Five mixed quantum/classical methods are tested: one mean-field approach (the coherent switching with decay of mixing method), two surface-hopping methods [the fewest switches with time uncertainty (FSTU) and FSTU with stochastic decay (FSTU/SD) methods], and two surface-hopping methods with zero-point energy (ZPE) maintenance [the FSTUSD+trajectory projection onto ZPE orbit (TRAPZ) and FSTUSD+minimal TRAPZ (mTRAPZ) methods]. We found a qualitative difference between final NH(2) internal energy distributions obtained for n(2)=0 and n(2)>1, as observed in experiments. Distributions obtained for n(2)=1 present an intermediate behavior between distributions obtained for smaller and larger n(2) values. The dynamics is found to be highly electronically nonadiabatic with all these methods. NH(2) internal energy distributions may have a negative energy tail when the ZPE is not maintained throughout the dynamics. The original TRAPZ method was designed to maintain ZPE in classical trajectories, but we find that it leads to unphysically high internal vibrational energies. The mTRAPZ method, which is new in this work and provides a general method for maintaining ZPE in either single-surface or multisurface trajectories, does not lead to unphysical results and is much less time consuming. The effect of maintaining ZPE in mixed quantum/classical dynamics is discussed in terms of agreement with experimental findings. The dynamics for n(2)=0 and n(2)=6 are also analyzed to reveal details not available from experiment, in particular, the time required for quenching of electronic excitation and the adiabatic energy gap and geometry at the time of quenching.     

Theoretical calculation of rate constants for the thermal isomerization from 1,2-butadiene to 1,3-butadiene

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A solvolysis model for 2-chloro-2-methyladamantane based on the linear solvation energy approach

Solvolysis/dehydrohalogenation rates of 2-chloro-2-methyladamantane (CMA) in 15 hydrogen-bond acidic and/or basic solvents are studied. The rates of reaction in these solvents have been correlated with the solvation equation developed by Kamlet, Abraham, and Taft. The linear solvation energy relationship (LSER) derived from this study is given by the following equation: log k = -5.409 + 2.219 + 2.505alpha(1) - 1.823beta(1) where , alpha(1), and beta(1) are the solvation parameters that measure the solvent dipolarity/polarizability, hydrogen-bond acidity (electrophilicity), and hydrogen-bond basicity (nucleophilicity). A high correlation coefficient (r = 0.996, SD = 0.191) was achieved. The cavity term, which includes the Hildebrand parameter for solvent cohesive energy density, delta(H), was not found to be statistically significant for this reaction substrate. The resulting equation allows calculated rates of reaction in other solvents and provides insight into the reaction pathway. In a previously reported correlation for another tertiary chloride, tert-butyl chloride (TBC), the coefficients for alpha(1) and are significantly larger and the coefficient for is statistically significant. In addition, the coefficient for beta(1) in the TBC correlation is positive, rather than negative, indicating that the transition states for TBC and CMA are significantly different. These results demonstrate why the uses of simple solvolytic correlation methods may be invalid even for comparisons of similar type substrates, e.g., tertiary chlorides. Also, these results provide confidence in the use of multiple linear regression analysis for predicting solvolytic rates in additional solvents.     

A kinetic investigation of the addition of diazomethane to styrenes. Role of dipolar aprotic solvents in predicting direction of dipole orientation

The addition of diazomethane to a series of substituted styrenes has been kinetically investigated with emphasis on polar, solvent, and solvation effects. Although the reaction is generally insensitive to solvent polarity, a sizeable substituent effect (ρ = +0.90) has been observed. Also, a sizeable increase in rate was generally observed in protic solvents such as water, and a considerable rate enhancement occurred in the case of nitrostyrene in the dipolar aprotic solvent, dimethylformamide. The results are discussed in terms of a concerted mechanism involving a partially-charged transition state II, with negative charge formation on the α-carbon of the styrene. The methoxystyrene offers an exception to the Hammett equation and the unexpectedly high rate constant for this compound could be discussed in terms of a possible participation of the highly nucleophilic resonance form of p-methoxystyrene and an α-addition via the transition state III. However, solvation effects in dimethylformamide (failure to obtain the anticipated rate increase) and the formation of a 3-substituted pyrazoline adduct from the cycloaddition reaction indicate steric control to predominate over electronic factors and β-addition to prevail unequivocally. It is proposed that solvation effects in protic solvents can be utilized to advantage in cycloaddition reactions leading to 1-pyrazolines, for which no other routes are available at the present time.