Bond Additivity Correction Research Articles

High-Throughput Predictions of Accurate Enthalpies of Formation for Larger Molecules Utilizing the Bond Difference Correction Method.

The prediction of standard enthalpies of formation (EOFs) for larger molecules involves a trade-off between accuracy and cost, often resulting in non-negligible errors. The connectivity-based hierarchy (CBH) and simple bond additivity correction (BAC) are two promising means for evaluating EOFs, although they cannot achieve strict chemical accuracy. Calculated errors in the CBH are confirmed from accumulated systematic errors associated with bond differences in chemical environments. On the basis of a new set of bond descriptors, our developed bond difference correction (BDC) method effectively solves incremental errors with molecular size and inability applications for aromatic molecules. To balance the accuracy between non-aromatic and aromatic molecules, a more accurate BAC-based method with unpaired electrons and p hybrid orbitals (BAC-EP) is developed. With the incorporation of the two methods above, strict chemical accuracy by the largest deviation is achieved at low costs. These universal, ultrafast, and high-throughput methods greatly contribute to self-consistent thermodynamic parameters in combustion mechanisms.

Method and automatic program for accurate thermodynamic data of reaction mechanisms for combustion modeling

Thermodynamic parameters are the main components of reaction mechanisms for combustion modeling. In this work, the high-precision and efficient methods are investigated to calculate the thermodynamic data of enthalpies of formation, entropies, and heat capacities. An automatic program of thermodynamic data off-line calculator (TDOC) is developed for given reaction mechanisms to efficiently get high-accuracy thermodynamic parameters. It is found the extrapolation of connectivity-based hierarchy (CBH) method can broaden the scope of application for larger molecules to achieve high-accuracy calculations for enthalpies of formation at CCSD(T)/CBS level with bond additivity correction (BAC). Moreover, the high-precision thermodynamic data must consider the contributions of the hindered-rotor corrections and conformational contributions. Finally, the simulations of ignition delay time and species concentration are performed by substituting the high-precision thermodynamic parameters. It reveals that the high-precision thermodynamic parameters can improve the performance of reaction mechanisms, in which the simulated ignition delay time and species concentration are closer to experimental data. We hope this work can shed new light on the construction of reaction mechanisms for combustion modeling.

Bond additivity corrections for CBS‐QB3 calculated standard enthalpies of formation of H, C, O, N, and S containing species

AbstractA prerequisite for the generation of detailed fundamental kinetic models is the availability of accurate thermodynamic properties. To address the scarcity of accurate experimental data, theoretical calculations can be used. The accuracy of these quantum chemistry methods for determination of thermodynamic properties can be improved by making use of empirical correction methods, such as the isodesmic bond additivity correction (BAC) method. In this work, ab initio calculations for a set of 371 molecules have been performed to determine a new set of BACs for the CBS‐QB3 level of theory. For each of these molecules also accurate experimental data, that is with an experimental uncertainty less than 3 kJ mol−1, is available. This broad dataset of hydrocarbons and heteroatomic compounds contains (non)cyclic molecules with a wide range of functional groups consisting of hydrogen, carbon, oxygen, nitrogen, and sulfur. The new set of 26 BAC parameters is obtained via linear regression analysis, minimizing the differences between experimental and corrected CBS‐QB3 values. The CBS‐QB3 method combined with BACs succeeds in approximating the experimental standard enthalpy of formation at 298 K with an accuracy of 4 kJ mol−1 for almost all species. The BACs reduce the mean absolute deviation for the complete dataset from 5.65 to 2.37 kJ mol−1, corresponding to a decrease of the root mean square deviation from 6.95 to 3.00 kJ mol−1.

Accurate Thermochemistry with Small Data Sets: A Bond Additivity Correction and Transfer Learning Approach.

Machine learning provides promising new methods for accurate yet rapid prediction of molecular properties, including thermochemistry, which is an integral component of many computer simulations, particularly automated reaction mechanism generation. Often, very large data sets with tens of thousands of molecules are required for training the models, but most data sets of experimental or high-accuracy quantum mechanical quality are much smaller. To overcome these limitations, we calculate new high-level data sets and derive bond additivity corrections to significantly improve enthalpies of formation. We adopt a transfer learning technique to train neural network models that achieve good performance even with a relatively small set of high-accuracy data. The training data for the entropy model are carefully selected so that important conformational effects are captured. The resulting models are generally applicable thermochemistry predictors for organic compounds with oxygen and nitrogen heteroatoms that approach experimental and coupled cluster accuracy while only requiring molecular graph inputs. Due to their versatility and the ease of adding new training data, they are poised to replace conventional estimation methods for thermochemical parameters in reaction mechanism generation. Since high-accuracy data are often sparse, similar transfer learning approaches are expected to be useful for estimating many other molecular properties.

Tuning Hydrogenated Silicon, Germanium, and SiGe Nanocluster Properties Using Theoretical Calculations and a Machine Learning Approach.

There are limited studies available that predict the properties of hydrogenated silicon-germanium (SiGe) clusters. For this purpose, we conducted a computational study of 46 hydrogenated SiGe clusters (Si xGe yH z, 1 < X + Y ≤ 6) to predict the structural, thermochemical, and electronic properties. The optimized geometries of the Si xGe yH z clusters were investigated using quantum chemical calculations and statistical thermodynamics. The clusters contained 6 to 9 fused Si-Si, Ge-Ge, or Si-Ge bonds, i.e., bonds participating in more than one 3- to 4-membered rings, and different degrees of hydrogenation, i.e., the ratio of hydrogen to Si/Ge atoms varied depending on cluster size and degree of multifunctionality. Our studies have established trends in standard enthalpy of formation, standard entropy, and constant pressure heat capacity as a function of cluster composition and structure. A novel bond additivity correction model for SiGe chemistry was regressed from experimental data on seven acyclic Si/Ge/SiGe species to improve the accuracy of the standard enthalpy of formation predictions. Electronic properties were investigated by analysis of the HOMO-LUMO energy gap to study the effect of elemental composition on the electronic stability of Si xGe yH z clusters. These properties will be discussed in the context of tailored nanomaterials design and generalized using a machine learning approach.

Database of Small Molecule Thermochemistry for Combustion

High-accuracy ab initio thermochemistry is presented for 219 small molecules relevant in combustion chemistry, including many radical, biradical, and triplet species. These values are critical for accurate kinetic modeling. The RQCISD(T)/cc-PV∞QZ//B3LYP/6-311++G(d,p) method was used to compute the electronic energies. A bond additivity correction for this method has been developed to remove systematic errors in the enthalpy calculations, using the Active Thermochemical Tables as reference values. On the basis of comparison with the benchmark data, the 3σ uncertainty in the standard-state heat of formation is 0.9 kcal/mol, or within chemical accuracy. An uncertainty analysis is presented for the entropy and heat capacity. In many cases, the present values are the most accurate and comprehensive numbers available. The present work is compared to several published databases. In some cases, there are large discrepancies and errors in published databases; the present work helps to resolve these problems.

Large Nonstatistical Branching Ratio in the Dissociation of Pentane-2,4-dione Radical Cation: An Ab Initio Direct Classical Trajectory Study

The dissociation of pentane-2,4-dione radical cation has been studied by ab initio direct classical trajectory calculations at the MP2/6-31G(d) level of theory. A bond additivity correction has been used to improve the MP2 potential energy surface (BAC-MP2). A microcanonical ensemble was constructed using quasiclassical normal-mode sampling by distributing 10 kcal/mol of excess energy above ZPE for the transition state for the tautomerization of the enol with a terminal double bond, 4-hydroxypent-4-en-2-one radical cation, to the diketo form. A total of 244 trajectories were run starting from this transition state, yielding pentane-2,4-dione radical cation and depositing energy in the terminal CC bond. As a result, the branching ratio for dissociation of the terminal CC bond versus the interior CC bonds is significantly larger than expected from RRKM theory. The branching ratio for the dissociation of the two interior CC bonds is ∼20:1, with the one closest to the activated methyl breaking more often. Since the two interior bonds are equivalent and should dissociate with equal probability, this branching ratio represents a very large deviation from statistical behavior. A simple kinetic scheme has been constructed to model the dissociation rates. The nonstatistical behavior is seen because the rate of energy flow within the molecule is comparable to or less than the rates of dissociation for the activated system. In addition to the expected dissociation products, some of the trajectories also lead to the formation of an ester-like product, prop-1-en-2-yl acetate radical cation.

Dissociation of Acetone Radical Cation (CH3COCH3+· → CH3CO+ + CH3·): An Ab Initio Direct Classical Trajectory Study of the Energy Dependence of the Branching Ratio

The nonstatistical dissociation of acetone radical cation has been studied by ab initio direct classical trajectory calculations at the MP2/6-31G(d) level of theory. A bond additivity correction has been used to improve the MP2 potential energy surface (BAC-MP2). The energy dependence of the branching ratio, dissociation kinetics, and translational energy distribution for the two types of methyl groups have been investigated using microcanonical ensembles and specific mode excitation. In each case, the dissociation favors the loss of the newly formed methyl group, in agreement with the experiments. For microcanonical ensembles, the branching ratios for methyl loss are calculated to be 1.43, 1.88, 1.70, and 1.50 for 1, 2, 10, and 18 kcal/mol of excess energy, respectively. The energy dependence of the branching ratio is seen more dramatically in the excitation of individual modes involving C-C-O bending. For modes 3 and 6, the branching ratio rises to 1.6 and 1.8-2.3 when 1 or 2 kcal/mol are added, respectively, but falls off when more energy is added. For mode 8, the branching ratio continues to rise monotonically from 1.5 to 2.76 when 1-8 kcal/mol of excess energy are added.

A Single Transition State Serves Two Mechanisms. The Branching Ratio for CH2O•- + CH3Cl on Improved Potential Energy Surfaces

The reaction of formaldehyde radical anion with methyl chloride, CH2O*- + CH3Cl, is an example in which a single transition state leads to two products: substitution at carbon (Sub(C), CH3CH2O* + Cl-) and electron transfer (ET, CH2O + CH3* + Cl-). The branching ratio for this reaction has been studied by ab initio molecular dynamics (AIMD). The energies of transition states and intermediates were computed at a variety of levels of theory and compared to accurate energetics calculated by the G3 and CBS-QB3 methods. A bond additivity correction has been constructed to improve the Hartree-Fock potential energy surface (BAC-UHF). A satisfactory balance between good energetics and affordable AIMD calculations can be achieved with BH&HLYP/6-31G(d) and BAC-UHF/6-31G(d) calculations. Approximately 200 ab initio classical trajectories were calculated for each level of theory with initial conditions sampled from a thermal distribution at 298 K at the transition state. Three types of trajectories were distinguished: trajectories that go directly to ET product, trajectories that go to Sub(C) product, and trajectories that initially go into the Sub(C) valley and then dissociate to ET products. The BH&HLYP/6-31G(d) calculations overestimate the number of nonreactive and direct ET trajectories because the transition state is too early. For the BH&HLYP and BAC-UHF methods, about one-third of the trajectories that initially go into the Sub(C) valley dissociate to ET products, compared to just over half with UHF/6-31G(d) in the earlier study. This difference can be attributed to a better value for the calculated energy release from the initial transition state and to an improved Sub(C) --> ET barrier height with the BH&HLYP and BAC-UHF methods.

Bond Additivity Corrections for G3B3 and G3MP2B3 Quantum Chemistry Methods

We have developed bond additivity correction (BAC) procedures for the G3-based quantum chemistry methods, G3B3 and G3MP2B3. We denote these procedures as BAC-G3B3 and BAC-G3MP2B3. We apply the procedures to compounds containing atoms from the first three rows of the periodic table including H, B, C, N, O, F, Al, Si, P, S, and Cl atoms. The BAC procedure applies atomic, molecular, and pairwise bond corrections to theoretical heats of formation of molecules. The BAC-G3B3 and BAC-G3MP2B3 procedures require parameters for each atom type but not for each bond type. These parameters have been obtained by minimizing the error between the BAC-G3B3 and BAC-G3MP2B3 predictions and the experimental heats of formation for a 155 molecule reference set, containing open and closed shell molecules representing various functional groups, multireference configurations, isomers, and degrees of saturation. As compared to former BAC-MP4, BAC-G2, and BAC-hybrid methods, BAC-G3B3 provides better agreement with experiment for a wider range of chemical moieties, including highly oxidized species involving SOx s, NOx s, POx s, and halogens. The BAC-G3B3 and BAC-G3MP2B3 procedures are applied to an extended test suite involving 273 compounds. We assess the overall quality of BAC-G3B3 with experiments and other theoretical approaches. For the reference set, the average error for the BAC-G3B3 results is 0.44 kcal/mol as compared to 0.82 kcal/mol for the raw G3B3. For the extended test set, the average error for the BAC-G3B3 results is 0.91 kcal/mol as compared to 1.38 kcal/mol for the raw G3B3. As compared to the other BAC procedures, the improved predictive capability of BAC-G3B3 and BAC-G3MP2B3 procedures is, to a large extent, due to the improved quality of G3-based methods resulting in much smaller BAC correction terms.

Thermochemistry of Silicon−Hydrogen Compounds Generalized from Quantum Chemical Calculations

Particulate contamination formed by homogeneous clustering reactions of silicon hydrides within silicon chemical vapor deposition processes is an important source of yield loss during semiconductor processing. On the other hand, intentional synthesis of silicon nanoparticles may be of great interest because of the unique optical and electronic properties of nanostructured silicon. Kinetic modeling can play an important role in developing a fundamental understanding of the particle clustering chemistry, and knowledge of the thermochemistry and reactivity of these silicon hydrides is necessary if a mechanistic kinetic model is to be constructed. Experimental measurements of thermochemical properties are usually expensive and difficult, and it is desirable to use computational quantum chemistry as an alternative. In this work, several theoretical methods were used to calculate thermochemical properties of silicon hydrides. Among the methods used, Gaussian-3 theory (G3) using the geometries from B3LYP density functional theory (B3LYP/6-31G(d)), referred to as G3//B3LYP, showed the most promising results with an average absolute deviation of 1.23 kcal/mol from experimental data for standard enthalpies of formation of small (<Si4) silicon hydrides. A series of calculations using G3//B3LYP was carried out on small to medium (<Si8) silicon hydrides to obtain thermochemical properties, and a bond additivity correction was incorporated to obtain more accurate thermochemical properties. A group additivity scheme was fit to these corrected values, allowing accurate estimation of the thermochemical properties of arbitrary silicon−hydrogen clusters. This generalization of the results is essential, since the many thousands of possible isomers of these molecules cannot be treated quantum chemically at even the least expensive levels of theory.

Systematic errors in DFT calculations of haloalkane heats of formation.

The B3LYP and B3PW91 density functionals were employed with a large [BS1 = 6-311+G(3df,2p)] and small [BS2 = 6-311G(d,p)] basis set to compute enthalpies of formation (at optimized MP2/6-31G(d) geometries and with scaled HF/6-31G(d) frequencies) in the following series of haloalkanes: (1) the 15 fluoro-, chloro-, and chlorofluoromethanes, (2) the 18 fluorinated and chlorinated ethanes. Similar to earlier higher level calculations on haloalkanes, the computed enthalpies exhibited very large, systematic deviations from experiment. It was found that these errors could be largely eliminated using a very simple Bond Additivity Correction (BAC) formula, Delta(f)H degrees (BAC) = Delta(f)H degrees (calc) - n(CX). Delta(CX) [X = F, Cl], in which the BAC parameters, Delta(CF) and Delta(CCl) were determined by fitting the equation to experimental data on the four fluoroethanes and chloroethanes, respectively. The resultant BAC corrected enthalpies of formation are in excellent agreement with experiment, with RMS deviations in the same range as quoted RMS errors in measured enthalpies. Therefore, this simple BAC procedure may be utilized to provide reliable semiquantitative estimates of enthalpies of formation in larger haloalkanes, for which higher level ab initio calculations are not feasible.

Bond Additivity Corrections for Quantum Chemistry Methods

New bond additivity correction (BAC) methods have been developed for the G2 method, BAC-G2, as well as for a hybrid density functional theory (DFT) Møller−Plesset (MP)2 method, BAC−hybrid. These BAC methods use a new form of BAC corrections, involving atomic, molecular, and bond-wise additive terms. These terms enable one to treat positive and negative ions as well as neutrals. The BAC-G2 method reduces errors in the G2 method due to nearest-neighbor bonds. The parameters within the BAC-G2 method only depend on atom types. Thus the BAC-G2 method can be used to determine the parameters needed by BAC methods involving lower levels of theory, such as BAC−hybrid and BAC-MP4. The BAC−hybrid method is expected to scale well for large molecules. The BAC−hybrid method uses the differences between the DFT and MP2 predictions as an indication of the method's accuracy, whereas the BAC-G2 method uses its internal methods (G1 and G2MP2) to accomplish this. A statistical analysis of the error in each of the methods is presented on the basis of calculations performed for large sets (more than 120) of molecules.

Understanding gas-phase reactions in the thermal CVD of hard coatings using computational methods

This article provides a short summary of the theoretical approaches to understanding gas-phase reactions. In particular, the quantum-chemical bond-additivity correction (BAC) method for predicting molecular thermochemistry of gas-phase molecules is described. A brief discussion of the use of RRKM methods for predicting the rates of unimolecular reactions and of ab initio methods for predicting the rates of bimolecular reactions is also presented. Finally, the question of when gas-phase reactions are likely to be important in CVD is discussed. Criteria are proposed for performing a first-order evaluation of the extent of precursor pyrolysis in the CVD of hard coatings. Examples from the CVD of titanium-containing species, boron nitride, and silicon carbide will be used for illustration.

Halon thermochemistry: Ab initio calculations of the enthalpies of formation of fluoroethanes

The ab initio G2, G2(MP2), CBS-4 and CBS-Q quantum mechanical protocols and the parameterized BAC-MP4 procedure were used to calculate the enthalpies of formation ( Δ f H 0) of ethane and the complete series of fluoroethanes, C 2H x F 6− x , x = 0−5. Results from all methods exhibited significant negative deviations from experiment. With the exception of the CBS-4 and BAC-MP4 procedures, the negative errors in the calculated enthalpies were observed to be linearly dependent upon the number of CF bonds in the molecule. Application of a bond additivity correction (BAC) parameter, Δ C F , derived in an earlier investigation of fluoro- and chlorofluoromethanes, removed some although not all of the systematic deviations. Introduction of a heavy atom interaction parameter, representing the effect of an attached carbon on the CF bond error, yielded corrected enthalpies which agree with experiment to within the reported uncertainties. The BAC-MP4 method, which has already been parameterized with generalized BACs, yields calculated enthalpies which average approximately 10 kJ mol −1 below the experimental values of Δ f H 0 in the fluoroethanes.

Theoretical Calculation of Thermochemistry for Molecules in the Si−P−H System

Ab initio molecular orbital calculations have been performed on species belonging to the Si-P-H system. These computations have been coupled to a bond additivity correction procedure to obtain heats of formation for 27 species. The Si-P single bond energy was found to be nominally about 300 kJ/mol, which is somewhat weaker than a Si-Si single bond. Multiple bond character in Si-P was found to be relatively weak. 11 refs., 7 tabs.

Theoretical characterization of the thermodynamics of the photoisomerizations of ethylene and propylene

A number of structures which may play a role in the thermal and triplet photochemistry of ethylene and propylene are calculated using ab initio methods. The energies and other properties obtained from these ab initio calculations are employed to calculate the heats of formation of the structures using the bond additivity correction (BAC) method of Carl Melius. Generally, the heats of formation appear to be accurate to within several kilocalories per mole, even for the triplet states and transition states encountered in this study. A final analysis reaches the conclusion that the triplet-sensitized photochemistries of ethylene and propylene occur through the hot ground states of these materials rather than through their respective triplet states.

An ab initio study of the structures and heats of formation of fluorosilanes cations (SiHmFn+, m + n = 1-4)

The equilibrium geometries of SiH{sub m}F{sub n}{sup +} (m + n = 1-4) were determined at the Hartree-Fock level by using the 3-21G and 6-31G* basis sets. The structures of SiH, SiF, and SiH{sub 2{minus}n}F{sub n}{sup +} resemble the neutral molecules; the tricoordinate cations are planar, whereas the neutral radicals are pyramidal. The SiH{sub 4{minus}n}F{sub n}{sup +} distort to form a complex between a silicon-containing cation and a neutral atom or diatom: SiH{sub 2}{sup +}-H{sub 2}, SiHF{sup +}-HF, SiHF{sup +}-HF, SiF{sub 2}{sup +}-HF, and SiF{sub 3}{sup +}-F are the lowest energy structures. Adiabatic ionization potentials and proton affinities were calculated at the MP4SDTQ/6-31G** level. Heats of formation were computed by the bond additivity correction method and from the ionization potentials and proton affinities.