The least squares calculation of the best values of the parameters of the Moffitt equation and of the Drude equation is examined. It is proved that the least squares evaluation of all three parameters of the Moffitt equation becomes indeterminate as the b(o) term approaches zero. Estimates of low helical content based on the Moffitt relationship are therefore also indeterminate and of dubious value. Both the size of b(o) and the range of wavelengths chosen affect the standard deviations of the parameters. The magnitude of the effects is illustrated by selected examples. The computer program OPTROT is available for evaluating the extent to which data may be correlated by the equations.

The purpose of this study has been to determine how well a consistent ab initio thermostatistical method reproduces experimental values of heat capacity and entropy. The method has been applied to calculation of heat capacity and entropy of a representative set of hydrocarbons that includes compounds consisting of multiple conformers. All Cp and S values are for the gaseous state at 1 atm; units are cal K-1 mol-1. A detailed sensitivity (error) analysis has been performed to determine the root mean square (rms) values of errors expected of the calculated values: these are 0.27 cal for Cp and 0.36 cal for entropy. In comparing calculated values with experimental values, it is necessary to consider also the uncertainties of the experimental data. When these are included, the expected rms values of Cp(experimental) - Cp(calculated) values at 298.15 K range from 0.21 to 0.73. For S(experimental) - S(calculated), they range from 0.36 to 0.72. Calculations with frequencies derived with the 6-31G(d,p) basis set and scaled by 0.91 yielded rms values for Cp(experimental) - Cp(calculated) of individual compounds from 0.14 to 0.84 cal and rms values for S(experimental) - S(calculated) of individual compounds from 0.07 to 1.11 cal. Calculated Cp values for 7 out of 16 compounds agree with experimental values within the rms uncertainty estimated for the compound, and 11 fall within twice that estimate. For entropy, the calculated values for 13 of 18 compounds agree with the very limited available experimental data within the rms estimated uncertainty for the compound, and 16 of 18 fall within twice the uncertainty.

The objective of this series of studies is to develop procedures for calculating high quality enthalpies of formation and differences of enthalpies of typical organic compounds. Can this be achieved using basis set/ electron correlation methods (BSECMs) of modest size so that the calculations are routinely applicable to molecules having 12 or more heavy atoms? The answer is a qualified "yes." The procedure I have explored is based on conversion of ab initio energies into formal steric enthalpy (FSE) values. FSE is the difference of the energy of a target molecule and Sigman(i)d(i), the sum of the energies of its constituent structural groups as defined by a set of standard molecules. FSE values are group isodesmic because the same numbers of each structural group appear in both the target molecule and in the summation. To a considerable extent, the isodesmic calculation cancels out errors due to limitations of BSECMs. FSE values can be converted to estimates of gas phase DeltaH(f)(omicron) values by a method related to the group increment method developed extensively by Benson and others. Energies derived with a number of BSECMs were explored. Of those evaluated, the most successful were MP2/6-31+G(d,p)//6-31G(d,p) and MP2/6-311+G(2df,2p)//6-3 1G(d,p). For 21 alcohols and ethers having a range of ring strain and steric congestion, the former gave differences between calculated DeltaH(f)(omicron)(g,298) Values and experimental values with a standard deviation of 0.56 kcal/mol and with a maximum deviation of 1.35, whereas the latter gave a standard deviation of 0.62 with a maximum deviation of 1.74. These numbers can be compared with an estimated standard deviation of the experimental DeltaH(f)(omicron) data of 0.44 kcal/mol and a maximum deviation of 1.22 for the same data set. Energies derived with the popular density functional B3LYP/G-31G(d,p) gave poorer results. The standard deviation was 1.25 and maximum deviation was 2.49. An important use of FSEs is in comparing enthalpies. While comparison of ab initio energies is restricted to conformers of the same molecule, comparison of FSEs gives a valid estimate of the difference of enthalpies of isomers as well. The difference of FSEs of unrelated molecules provides an estimate of the difference of strain enthalpies, and this may be converted to an estimate Of the difference of total enthalpies by correcting for the bond enthalpy terms as described in the text. These comparisons pertain to hypothetical compounds that consist solely of the molecules being compared.

A semitheoretical calculation of enthlapies of formation has been applied to alcohols and ethers. The calculation involves two steps. In the first step the ab initio energy for the conformer of lowest energy is converted into an estimate of the formal steric enthalpy (FSE). In the second step the FSE is combined with the formal bond enthalpy (FBE) to generate an estimate of Delta H(f)degrees. The group increments for calculating the FEE values are derived from experimental enthalpies of formation. FSE values and FEE values are defined in terms of standard molecules. Calibration requires minimal calculation and the procedure is readily generalized to other classes of compounds. The calculation is group isodesmic. Three basis sets were used: 3-21G, 6-31G*, and 6-31G**. Electron correlation was performed with single point estimates using MP2 (Moeller-Plesset, truncated at the quadratic expansion) with geometry optimized with HF 6-31G**. For a selection of molecules geometry optimizations were also performed with the MP2/6-31G** procedure. Delta H(f)degrees values derived using the 6-31G** basis set with a single point MP2 estimation of electron correlation agree with experimental Delta H(f)degrees values within the reasonable standard deviation of 0.55 kcal/mol for 14 molecules, including strained cyclic ethers and highly strained acyclic examples. Examination of the conformer families provides information useful for interpretation of steric effects in synthetic reactions. Average relative energy differences for four important torsional sequences expressed as gauche minus trans energy differences are 0.8 kcal/mol for C-C-C-C (literature), 1.4 for C-C-O-C, 0.6 for O-C-C-O, and -0.5 for C-C-C-O but -1.2 for the last sequence if the terminal carbon atom has an attached oxygen atom. Intramolecular hydrogen bonding effects are important (3 kcal/mol) for some conformers of 1,2-diols and reach 3 kcal/mol for 1,3-diols.

This study describes the theoretical ab initio calculation of entropy, heat capacity, and heat content for a series of alkanes by procedures that make no use of adjustable parameters. Frequencies calculated with the basis sets, 3-21G, 6-31G*, and 6-31G** and scaled by factors of 0.89 and 0.90 were used to obtain theoretical entropy values that agree well with reported values. Over a temperature range from room temperature to at least 800 It the differences between T Delta S based on calculated and literature values of Delta S are generally less than 0.3 kcal/mol. Agreement between theoretical and experimental heal capacities and heat contents (H-tau(o) - H-o(o)) is also good. Results for compounds that exist as mixtures of conformers give as good results as do compounds that exist as a single conformer.

Calculation of enthalpies of formation from steric energies obtained by molecular mechanics is usually based on the equation Delta H-f - SM = Sigma n(i)a(i) + SE or a variant; SE is the ''steric energy'' given by a molecular mechanics calculation. A similar equation has been used for ab initio calculations; SE would be replaced by the ab initio energy. There are four serious limitations in interpreting the calculated Delta H-f degrees values: (1) Differences in calculated Delta H-f degrees values obtained with different force fields (or basis sets) arise from differences in calibration sets as well as from differences in the force fields (or basis sets) themselves. (2) Any change in the parameters of a force field that lead to revised SE values for a given set of molecules will necessitate recalibration of the al values if calculated Delta H-f degrees values are to be valid. Owing to the large sizes of calibration sets customarily used and, usually, to lack of documentation, recalibration is impractical or impossible and is almost never done. (3) Calculation of Delta H-f degrees requires SM, a correction for the energy contributed by conformers other than the global minimum. The SM (or equivalent) values used in a given study are not generally published. (4) Calibration procedures distribute errors among all compounds of a calibration set and hence diminish or conceal important trends among errors. These several limitations reduce the significance of comparisons among Delta H-f degrees values calculated in different laboratories or within the same laboratory using different force fields. The limitations can be overcome by separating the calculation of Delta H-f degrees into two parts, a larger part (usually), the formal group enthalpy, which is independent of force field or basis set and a smaller part, the formal steric enthalpy (FSE), which is derived through application of the force field or basis set. Both parts are defined in terms of standard reference molecules. The method may be characterized as an extended type of isodesmic calculation. The FSE method has several advantages. First is that calibrations are based on minimal sets of clearly defined standard molecules. This feature facilitates both portability and ease of calibration and recalibration. Second, there is significant cancellation of errors arising from limitations of force field or basis set, an advantage inherent in isodesmic methods. Third is that FSE values provide a tool for making direct comparisons of performances of force fields or of basis sets. Since FSE values are defined in terms of defined standard molecules, every method of calculation must in principle give the identical FSE value for a given molecule. Moreover, useful comparisons of differences of Delta H-f degrees values are possible even though SM values or experimental Delta H-f degrees data are lacking. In the present study the FSE method has been used to evaluate the performance of several basis sets in calculation of FSE values and of Delta H-f degrees values of alkanes and cycloalkanes. The study has turned up an unresolved inconsistency in the performance of the basis sets between acyclic and cyclic alkanes. A similar inconsistency had been noted previously with some force fields. An analysis is presented of the validity of estimating zero point energies and Delta H(0-298) values as sums of increments. Results obtained with alkanes are of special significance since most molecules consist primarily of hydrocarbon subunits.

Steric energies calculated by molecular mechanics are used to estimate enthalpies of formation and differences and double differences of enthalpies of formation. The underlying principles and the precautions necessary to obtain valid results are analyzed. To compare results of calculations with two different force fields SE values are of little use, but they may be normalized to formal steric anthalpy (FSE) values which do provide a direct and unbiased comparison. Procedures are described for calculating FSE values with the MM2 and MMS force fields. It is strongly recommended that results of molecular mechanics calculations be reported in terms of FSE values so that calculations in different laboratories with the same or with different force fields may be directly compared.

This study is a critical evaluation of experimental values of formal steric enthalpies of alcohols and ethers, gas phase, 25-degrees-C, derived from published values of enthalpies of formation. These data can serve as primary values for calibration of force fields used in molecular mechanics.

Sets of standard olefins have been selected for defining formal steric enthalpies. All possible olefins can be described in terms of 17 structural elements in addition to the four structural elements used to describe alkanes. It is possible to define definitive FBE increments for 11 of these, and reasonable estimates may be assigned to the rest. For 76 olefins for which FSE values have been assigned or estimated, the standard deviation of the difference between the experimental FSE value and the assigned or estimated value os 0.44 kcal/mol. This value is the same as the reported average uncertainties of the enthalpy of formation data (0.43).

This study is a critical evaluation of experimental values of formal steric enthalpies derived from published values of enthalpies of formation of aldehydes, ketones, esters, and acids, gas phase, 25-degrees-C. These data may be useful for calibration of force fields.

This study makes a critical evaluation of experimental values of formal steric enthalpies derived from published values of enthalpies of formation of alkanes and cycloalkanes (gas phase, 298 K). These provide primary data for calibration of force fields used in molecular mechanics.

This is a proposal for development of modular molecular mechanics and molecular dynamics programs and for standardization of the format of force fields and of the format of molecular descriptions. This capability will require standardization of certain arrays and variables so that an MM/MD “engine” can be designed to use packages of logic subroutines and computational subroutines. The objective is to facilitate the widespread participation of many groups in the development of better force fields and better programs so that we have the capability of working reliably with a variety of force fields.