Scaling factors for obtaining fundamental vibrational frequencies, low-frequency vibrations, zero-point vibrational energies (ZPVE), and thermal contributions to enthalpy and entropy from harmonic frequencies determined at 19 levels of theory have been derived through a least-squares approach. Semiempirical methods (AM1 and PM3), conventional uncorrelated and correlated ab initio molecular orbital procedures [Hartree−Fock (HF), Moller−Plesset (MP2), and quadratic configuration interaction including single and double substitutions (QCISD)], and several variants of density functional theory (DFT:  B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91) have been examined in conjunction with the 3-21G, 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-311G(d,p), and 6-311G(df,p) basis sets. The scaling factors for the theoretical harmonic vibrational frequencies were determined by a comparison with the corresponding experimental fundamentals utilizing a total of 1066 individual vibrations. Scaling factors suitable for low-frequency vib...

Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Møller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors

"Chemists familiar with conventional quantum mechanics will applaud and benefit greatly from this particularly instructive, thorough and clearly written exposition of density functional theory: its basis, concepts, terms, implementation, and performance in diverse applications. Users of DFT for structure, energy, and molecular property computations, as well as reaction mechanism studies, are guided to the optimum choices of the most effective methods. Well done!" Paul von RaguE Schleyer "A conspicuous hole in the computational chemist's library is nicely filled by this book, which provides a wide-ranging and pragmatic view of the subject.[...It] should justifiably become the favorite text on the subject for practioneers who aim to use DFT to solve chemical problems." J. F. Stanton, J. Am. Chem. Soc. "The authors' aim is to guide the chemist through basic theoretical and related technical aspects of DFT at an easy-to-understand theoretical level. They succeed admirably." P. C. H. Mitchell, Appl. Organomet. Chem. "The authors have done an excellent service to the chemical community. [...] A Chemist's Guide to Density Functional Theory is exactly what the title suggests. It should be an invaluable source of insight and knowledge for many chemists using DFT approaches to solve chemical problems." M. Kaupp, Angew. Chem.

A Chemist's Guide to Density Functional Theory

Gaussian-3 theory (G3 theory) for the calculation of molecular energies of compounds containing first (Li–F) and second row (Na–Cl) atoms is presented. This new theoretical procedure, which is based on ab initio molecular-orbital theory, modifies G2 theory [J. Chem. Phys. 94, 7221 (1991)] in several ways including a new sequence of single point energy calculations using different basis sets, a new formulation of the higher level correction, a spin–orbit correction for atoms, and a correction for core correlation. G3 theory is assessed using 299 energies from the G2/97 test set including enthalpies of formation, ionization potentials, electron affinities, and proton affinities. This new procedure corrects many of the deficiencies of G2 theory. There is a large improvement for nonhydrogen systems such as SiF4 and CF4, substituted hydrocarbons, and unsaturated cyclic species. Core-related correlation is found to be a significant factor, especially for species with unsaturated rings. The average absolute devi...

Gaussian-3 (G3) theory for molecules containing first and second-row atoms

The recently introduced complete basis set, CBS-Q, model chemistry is modified to use B3LYP hybrid density functional geometries and frequencies, which give both improved reliability (maximum error for the G2 test set reduced from 3.9 to 2.8 kcal/mol) and increased accuracy (mean absolute error reduced from 0.98 to 0.87 kcal/mol), with little penalty in computational speed. The use of a common method for geometries and frequencies makes the modified model applicable to transition states for chemical reactions.

A complete basis set model chemistry. VI. Use of density functional geometries and frequencies

The basis-set convergence of the electronic correlation energy in the water molecule is investigated at the second-order Mo/ller–Plesset level and at the coupled-cluster singles-and-doubles level with and without perturbative triples corrections applied. The basis-set limits of the correlation energy are established to within 2 mEh by means of (1) extrapolations from sequences of calculations using correlation-consistent basis sets and (2) from explicitly correlated calculations employing terms linear in the interelectronic distances rij. For the extrapolations to the basis-set limit of the correlation energies, fits of the form a+bX−3 (where X is two for double-zeta sets, three for triple-zeta sets, etc.) are found to be useful. CCSD(T) calculations involving as many as 492 atomic orbitals are reported.

Basis-set convergence of correlated calculations on water

It is shown that localization is necessary to preserve size consistency in nonlinear extrapolations of molecular energies. We demonstrate that the unphysical behavior of Mulliken populations obtained from extended basis set wave functions can lead to incomplete localization of orbitals by the Pipek–Mezey population localization method, and introduce a modification to correct this problem. The new localization procedure, called minimum population localization, is incorporated into the CBS-QB3 and the new CBS-4M model chemistries, and their performance is assessed on the G2/97 test set. The errors found for CBS-QB3 are comparable with those for the G3 and G3(MP2) (mean absolute deviation of 1.10, 0.94, and 1.21 kcal/mol, respectively, on the G2/97 test set). The CBS-4M is less accurate than the other models (mean absolute deviation of 3.26 kcal/mol on the G2/97 test set), but can be applied to much larger systems. The modified localization method resolves several problem cases found with CBS-4 and improves the reliability of CBS-QB3.

A complete basis set model chemistry. VII. Use of the minimum population localization method

The major source of error in most ab initio calculations of molecular energies is the truncation of the one‐electron basis set. Extrapolation to the complete basis set second‐order (CBS2) limit using the N−1 asymptotic convergence of N‐configuration pair natural orbital (PNO) expansions can be combined with the use of relatively small basis sets for the higher‐order (i.e., MP3, MP4, and QCI) correlation energy to develop cost effective computational models. Following this strategy, three new computational models denoted CBS‐4, CBS‐q, and CBS‐Q, are introduced. The mean absolute deviations (MAD) from experiment for the 125 energies of the G2 test set are 2.0, 1.7, and 1.0 kcal/mol, respectively. These results compare favorably with the MAD for the more costly G2(MP2), G2, and CBS‐QCI/APNO models (1.6, 1.2, and 0.5 kcal/mol, respectively). The error distributions over the G2 test set are indistinguishable from Gaussian distribution functions for all six models, indicating that the rms errors can be interpreted in the same way that experimental uncertainties are used to assess reliability.However, a broader range of examples reveals special difficulties presented by spin contamination, high molecular symmetry, and localization problems in molecules with multiple lone pairs on the same atom. These characteristics can occasionally result in errors several times the size expected from the Gaussian distributions. Each of the CBS models has a range of molecular size for which it is the most accurate computational model currently available. The largest calculations reported for these models include: The CBS‐4 heat of formation of tetranitrohydrazine (91.5±5 kcal/mol), the CBS‐4 and CBS‐q isomerization energies for the conversion of azulene to naphthalene (ΔHcalc=−35.2±1.0 kcal/mol, ΔHexp=−35.3±2.2 kcal/mol), and the CBS‐Q heat of formation of SF6 (ΔHcalc=−286.6±1.3 kcal/mol, ΔHexp=−288.3±0.2 kcal/mol). The CBS‐Q value for the dissociation energy of a C–H bond in benzene (113.1±1.3 kcal/mol) is also in agreement with the most recent experimental result (112.0±0.6 kcal/mol). The CBS‐QCI/APNO model is applicable to the prediction of the C–H bond dissociation energies for the primary (100.7±0.7 kcal/mol calc.) and secondary (97.7±0.7 kcal/mol calc., 97.1±0.4 kcal/mol exp.) hydrogens of propane.

A complete basis set model chemistry. V. Extensions to six or more heavy atoms

An improved complete basis set‐quadratic configuration interaction/atomic pair natural orbital (CBS‐QCI/APNO) model is described in this paper. It provides chemical energy differences (i.e., D0 I.P., and E.A.) with a mean absolute error of 0.53 kcal/mol for the 64 first‐row examples from the G2 test set, and is computationally feasible for species with up to three first‐row atoms. A set of 20 CBS‐QCI/APNO bond dissociation energies of hydrocarbons also agree with known experimental values to within less than 1 kcal/mol. Calculations on the cyclopropenyl radical and cyclopropenylidene provide new dissociation energies which are in accord with an interpretation of the thermochemistry emphasizing ring strain and aromaticity.

A complete basis set model chemistry. IV. An improved atomic pair natural orbital method

We have reexamined several high-accuracy Gaussian-2, complete basis set and density functional methods for computational thermochemistry (in order of increasing speed): G2, G2(MP2), CBS-Q, G2(MP2,SVP), CBS-q, CBS-4, and B3LYP/6-311+G(3df,2p) We have employed ΔfH2980 for the “extended G2 neutral test set” for this comparison Several errors in previous studies have been corrected and experimental spin-orbit interactions have been included in all calculated atomic energies The mean absolute deviations from experiment are 143, 176, 119, 164, 234, 266, and 343 kcal/mol, respectively The maximum deviations from experiment are 106, 88, 81, 94, 114, 129, and 241 kcal/mol respectively The species responsible for these maximum errors are in order: SiF4, SiF4, Cl2C=CCl2, F2C=CF2, ClF3, ClF3, and SiCl4 All seven methods have relatively large errors for bonds to halogens, but these errors are sufficiently systematic to benefit from empirical corrections After a discussion of ill conditioning in th

Joseph W. Ochterski

Papers

A complete basis set model chemistry. VI. Use of density functional geometries and frequencies

A complete basis set model chemistry. VII. Use of the minimum population localization method

A complete basis set model chemistry. V. Extensions to six or more heavy atoms

A complete basis set model chemistry. IV. An improved atomic pair natural orbital method

Calibration and comparison of the Gaussian-2, complete basis set, and density functional methods for computational thermochemistry