^{1}, Arteum D. Bochevarov

^{1}and Richard A. Friesner

^{1,a)}

### Abstract

This paper is a logical continuation of the 22 parameter, localized orbital correction (LOC) methodology that we developed in previous papers [R. A. Friesner *et al.*, J. Chem. Phys.125, 124107 (2006); E. H. Knoll and R. A. Friesner, J. Phys. Chem. B110, 18787 (2006).] This methodology allows one to redress systematic density functional theory(DFT) errors, rooted in DFT’s inherent inability to accurately describe nondynamical correlation. Variants of the LOC scheme, in conjunction with B3LYP (denoted as B3LYP-LOC), were previously applied to enthalpies of formation, ionization potentials, and electron affinities and showed impressive reduction in the errors. In this paper, we demonstrate for the first time that the B3LYP-LOC scheme is robust across different basis sets [, , cc-pVTZ, and aug-cc-pVTZ] and reaction types (atomization reactions and molecular reactions). For example, for a test set of 70 molecular reactions, the LOC scheme reduces their mean unsigned error from 4.7 kcal/mol [obtained with ] to 0.8 kcal/mol. We also verified whether the LOC methodology would be equally successful if applied to the promising M05-2X functional. We conclude that although M05-2X produces better reactionenthalpies than B3LYP, the LOC scheme does not combine nearly as successfully with M05-2X than with B3LYP. A brief analysis of another functional, M06-2X, reveals that it is more accurate than M05-2X but its combination with LOC still cannot compete in accuracy with B3LYP-LOC. Indeed, B3LYP-LOC remains the best method of computing reactionenthalpies.

This work was supported in part by grants from the NIH (Grant No. GM40526) and DOE (Grant No. DE-FG02–90ER-14162).

I. INTRODUCTION

II. THE LOCs OVERVIEW

III. COMPUTATIONAL DETAILS

IV. RESULTS

A. Atomization reactions

B. Molecular reactions

V. DISCUSSION

VI. CONCLUSIONS

### Key Topics

- Density functional theory
- 32.0
- Enthalpy
- 25.0
- Formation enthalpy
- 25.0
- Atom reactions
- 24.0
- Basis sets
- 24.0

## Figures

The histogram of errors of across the G3 data set in the aug-cc-pVTZ basis: the white and black bars represent the pure and the LOC-corrected functionals, respectively.

The histogram of errors of across the G3 data set in the aug-cc-pVTZ basis: the white and black bars represent the pure and the LOC-corrected functionals, respectively.

The histogram of errors of across the G3 data set in the basis: the white and black bars represent the pure and the LOC-corrected functionals, respectively.

The histogram of errors of across the G3 data set in the basis: the white and black bars represent the pure and the LOC-corrected functionals, respectively.

## Tables

The 22 parameters fit to both the extended G2 and G3 data sets for each basis set using the classic B3LYP hybrid functional.

The 22 parameters fit to both the extended G2 and G3 data sets for each basis set using the classic B3LYP hybrid functional.

The MUEs of enthalpies of formation at 298.15 K of Pople’s extended G2 and full G3 set in kcal/mol. Pure values are the MUEs without any LOCs. denotes the use of LOCs fit to the extended G2 data set. denotes the use of LOCs fit to the entire G3 data set.

The MUEs of enthalpies of formation at 298.15 K of Pople’s extended G2 and full G3 set in kcal/mol. Pure values are the MUEs without any LOCs. denotes the use of LOCs fit to the extended G2 data set. denotes the use of LOCs fit to the entire G3 data set.

The MUEs of enthalpies of formation at 298.15 K of Pople’s complement of G2 with respect to G3 (75 compounds in total) in kcal/mol. The error is defined as the experimental value minus the DFT value. Pure values are the MUEs without any LOCs. denotes the use of LOCs fit to the extended G2 data set. denotes the use of LOCs fit to the entire G3 data set.

The MUEs of enthalpies of formation at 298.15 K of Pople’s complement of G2 with respect to G3 (75 compounds in total) in kcal/mol. The error is defined as the experimental value minus the DFT value. Pure values are the MUEs without any LOCs. denotes the use of LOCs fit to the extended G2 data set. denotes the use of LOCs fit to the entire G3 data set.

The 22 parameters fit to both the extended G2 and G3 data sets for each basis set using the classic M05-2X hybrid functional.

The 22 parameters fit to both the extended G2 and G3 data sets for each basis set using the classic M05-2X hybrid functional.

The MRG2-TRN set and the errors of the constituent reactions obtained with B3LYP and M05-2X in the basis set. The errors are given in kcal/mol. The error is defined as the experimental value minus the DFT value. All errors are with respect to the reaction enthalpies obtained from the experimental enthalpies of formation of the individual compounds. The coefficients used in the LOC scheme were obtained from the solution of the linear system constructed after the MRG2-TRN set.

The MRG2-TRN set and the errors of the constituent reactions obtained with B3LYP and M05-2X in the basis set. The errors are given in kcal/mol. The error is defined as the experimental value minus the DFT value. All errors are with respect to the reaction enthalpies obtained from the experimental enthalpies of formation of the individual compounds. The coefficients used in the LOC scheme were obtained from the solution of the linear system constructed after the MRG2-TRN set.

The performance of different parametrizations of the LOC approach on various sets of atomization and molecular reactions with compounds from G2 set only. The errors are given in kcal/mol. The coefficients of the LOC parametrization were first found by solving a system of linear equations in the least-square sense. Then these coefficients were used in the application of the LOC scheme to a set of reactions. The first row of the table indicates the equations from which the coefficients were derived, whereas the second row shows the reactions to which the coefficients were applied. A stands for the atomization reactions of the G2 set (147 reactions), TRN stands for the MRG2 training set (90 reactions), and TST stands for the MRG2 test set (60 reactions). The MUEs of the enthalpies of formation for the LOC scheme are compared to the analogous values of the pure (without LOC) DFT method.

The performance of different parametrizations of the LOC approach on various sets of atomization and molecular reactions with compounds from G2 set only. The errors are given in kcal/mol. The coefficients of the LOC parametrization were first found by solving a system of linear equations in the least-square sense. Then these coefficients were used in the application of the LOC scheme to a set of reactions. The first row of the table indicates the equations from which the coefficients were derived, whereas the second row shows the reactions to which the coefficients were applied. A stands for the atomization reactions of the G2 set (147 reactions), TRN stands for the MRG2 training set (90 reactions), and TST stands for the MRG2 test set (60 reactions). The MUEs of the enthalpies of formation for the LOC scheme are compared to the analogous values of the pure (without LOC) DFT method.

The performance of the M06-2X functional and its LOC analog on the G2 set. The errors are given in kcal/mol.

The performance of the M06-2X functional and its LOC analog on the G2 set. The errors are given in kcal/mol.

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