George A. Petersson

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

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. II. Open‐shell systems and the total energies of the first‐row atoms

The major source of error in most ab initio calculations of molecular energies is the truncation of the one‐electron basis set. An open‐shell complete basis set (CBS) model chemistry, based on the unrestricted Hartree–Fock (UHF) zero‐order wave function, is defined to include corrections for basis set truncation errors. The total correlation energy for the first‐row atoms is calculated using the unrestricted Mo/ller–Plesset perturbation theory, the quadratic configuration interaction (QCI) method, and the CBS extrapolation. The correlation energies of the atoms He, Li, Be, B, C, N, O, F, and Ne, calculated using atomic pair natural orbital (APNO) basis sets, vary from 85.1% to 95.5% of the experimental correlation energies. However, extrapolation using the asymptotic convergence of the pair natural orbital expansions retrieves from 99.3% to 100.6% of the experimental correlation energies for these atoms. The total extrapolated energies (ESCF+Ecorrelation) are then in agreement with experiment to within ±0...

A complete basis set model chemistry. I. The total energies of closed‐shell atoms and hydrides of the first‐row elements

The major source of errror in most ab initio calculations of molecular energies is the truncation of the one‐electron basis set. A complete basis set model chemistry is defined to include corrections for basis set truncation errors. This model uses double zeta plus polarization level atomic pair natural orbital basis sets to calculate molecular self‐consistent‐field (SCF) energies and correlation energies. The small corrections to give the complete basis set SCF energies are then estimated using the l−6 asymptotic convergence of the multicenter angular momentum expansion. The calculated correlation energies of the atoms He, Be, and Ne, and of the hydrides LiH, BH3, CH4, NH3, H2O, and HF, using the double zeta plus polarization basis sets vary from 83.0% to 91.2% of the experimental correlation energies. However, extrapolation of each of the pair energies and pair‐coupling terms to the complete basis set values using the asymptotic convergence of pair natural orbital expansions retrieves from 99.5±0.7% to ...

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

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. V: EXTENSIONS TO SIX OR MORE HEAVY ATOMS

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 interpre...

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

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. III. The complete basis set‐quadratic configuration interaction family of methods

The major source of error in most ab initio calculations of molecular energies is the truncation of the one‐electron basis set. A family of complete basis set (CBS) quadratic CI (QCI) model chemistries is defined to include corrections for basis set truncation errors. These models use basis sets ranging from the small 6‐31 G°° double zeta plus polarization (DZ+P) size basis set to the very large (14s9p4d2f,6s3p1d)/[6s6p3d2f,4s2p1d] atomic pair natural orbital basis set. When the calculated energies are compared with the experimental energies of the first‐row atoms and ions and the first‐row diatomics and hydrides H2, LiH, Li2, CH4, NH3, H2O, HF, LiF, N2, CO, NO, O2, and F2, two very promising new model chemistries emerge. The first is of comparable accuracy, but more than ten times the speed of the G1 model of Pople and co‐workers. The second is less than one‐tenth the speed of the G1 model, but reduces the root‐mean‐square (rms) errors in ionization potentials (IPs), electron affinities (EAs), and D0’s t...

Complete basis set correlation energies. I. The asymptotic convergence of pair natural orbital expansions

An expression for the ’’correlation energy’’ of a multiconfiguration wave function is developed using perturbation theory. The asymptotic form of this expression for an N‐configuration pair natural orbital expansion is Error(N×N)?(Σμ = 1NCμ)2 (−225/4608)N−1. The asymptotic form attributes the dominant variation in multiconfiguration pair correlation errors to an interference effect between low‐lying natural orbitals. Three levels of extrapolation based on the asymptotic convergence of pair natural orbital expansions are examined. The first requires separate calculations with 5 and 14 natural orbitals. When applied to the helium atom, for which E(5) = −2.897 484 and E(14) = −2.901 697, the extrapolated value, E = −2.903 724, is accurate to within 0.05% of the error from the 14 natural orbital wave function (i.e., the absolute accuracy is ≲0.000 001 hartree). The second extrapolation requires separate calculations with 5 and 14 pair MCSCF configurations and is accurate to within 2% of the MCSCF (14) error (...

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

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 1.43, 1.76, 1.19, 1.64, 2.34, 2.66, and 3.43 kcal/mol, respectively. The maximum deviations from experiment are 10.6, 8.8, 8.1, 9.4, 11.4, 12.9, and 24.1 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...

A Density Functional with Spherical Atom Dispersion Terms.

A new hybrid density functional, APF, is introduced, which avoids the spurious long-range attractive or repulsive interactions that are found in most density functional theory (DFT) models. It therefore provides a sound baseline for the addition of an empirical dispersion correction term, which is developed from a spherical atom model (SAM). The APF-D empirical dispersion model contains nine adjustable parameters that were selected based on a very small training set (15 noble gas dimers and 4 small hydrocarbon dimers), along with two computed atomic properties (ionization potential and effective atomic polarizability) for each element. APF-D accurately describes a large portion of the potential energy surfaces of complexes of noble gas atoms with various diatomic molecules involving a wide range of elements and of dimers of small hydrocarbons, and it reproduces the relative conformational energies of organic molecules. The accuracy for these weak interactions is comparable to that of CCSD(T)/aug-cc-pVTZ calculations. The accuracy in predicting the geometry of hydrogen bond complexes is competitive with other models involving DFT and empirical dispersion.