^{1}, Hrant P. Hratchian

^{1}and Krishnan Raghavachari

^{1,a)}

### Abstract

Hybrid QM:QM (quantum mechanics:quantum mechanics) and QM:MM (quantum mechanics:molecular mechanics) methods are widely used to calculate the electronic structure of large systems where a full quantum mechanical treatment at a desired high level of theory is computationally prohibitive. The ONIOM (our own -layer integrated molecular orbital molecular mechanics) approximation is one of the more popular hybrid methods, where the total molecular system is divided into multiple layers, each treated at a different level of theory. In a previous publication, we developed a novel QM:QM electronic embedding scheme within the ONIOM framework, where the model system is embedded in the external Mulliken point charges of the surrounding low-level region to account for the polarization of the model system wave function. Therein, we derived and implemented a rigorous expression for the embedding energy as well as analytic gradients that depend on the derivatives of the external Mulliken point charges. In this work, we demonstrate the applicability of our QM:QM method with point charge embedding and assess its accuracy. We study two challenging systems—zinc metalloenzymes and silicon oxide cages—and demonstrate that electronic embedding shows significant improvement over mechanical embedding. We also develop a modified technique for the energy and analytic gradients using a generalized asymmetric Mulliken embedding method involving an unequal splitting of the Mulliken overlap populations to offer improvement in situations where the Mulliken charges may be deficient.

This work was supported by the National Science Foundation (Grant No. CHE-0616737). H.P.H. also acknowledges the Indiana University (Department of Chemistry) Ernest R. Davidson Fellowship for financial support.

I. INTRODUCTION

II. METHODS

A. Generalized asymmetric Mulliken embedding (GAME): Energy and gradients

III. ASSESSMENT OF THE ONIOM-QM:QM MULLIKEN POINT CHARGE EMBEDDING SCHEME

IV. CONCLUSIONS

### Key Topics

- Chemical bonds
- 17.0
- Exoelectron emission
- 17.0
- Zinc
- 17.0
- Polarization
- 7.0
- Protons
- 7.0

## Figures

Models used for the ONIOM QM:QM EE method—the high-level region is denoted as ball and stick representation and low-level region as tube rendering. (a) Proton transfer in a complex. (b) Removal of water from a complex.

Models used for the ONIOM QM:QM EE method—the high-level region is denoted as ball and stick representation and low-level region as tube rendering. (a) Proton transfer in a complex. (b) Removal of water from a complex.

PESs for the proton transfer between two water molecules in a complex at different model chemistries; high-level target, low-level, ONIOM mechanical embedding (ME) and ONIOM point charge embedding (PT). (a) , (b) , and (c) . In (a), the PES calculated by ONIOM point charge embedding almost coincides with the high-level target PES.

PESs for the proton transfer between two water molecules in a complex at different model chemistries; high-level target, low-level, ONIOM mechanical embedding (ME) and ONIOM point charge embedding (PT). (a) , (b) , and (c) . In (a), the PES calculated by ONIOM point charge embedding almost coincides with the high-level target PES.

PESs for the removal of water molecule from a complex at the model chemistry. Note the catastrophic failure of the ONIOM-ME method with increasing Zn–O distance.

PESs for the removal of water molecule from a complex at the model chemistry. Note the catastrophic failure of the ONIOM-ME method with increasing Zn–O distance.

PESs for the removal of from the complex in the gas phase. The squares indicate the surface that is the high-level target, the circles indicate regular Mulliken point charge embedding at the level, the triangles show point charge embedding with 70% of the electron overlap population on Zn and 30% on N of the imidazole ligands, and the stars indicate the case with 30% on Zn and 70% on N.

PESs for the removal of from the complex in the gas phase. The squares indicate the surface that is the high-level target, the circles indicate regular Mulliken point charge embedding at the level, the triangles show point charge embedding with 70% of the electron overlap population on Zn and 30% on N of the imidazole ligands, and the stars indicate the case with 30% on Zn and 70% on N.

The three ways [(A)–(C)] used to divide the entire hydroxylated spherosiloxane cluster into two layers: The high-level region is indicated as ball and stick representation and the low-level region as tube rendering.

The three ways [(A)–(C)] used to divide the entire hydroxylated spherosiloxane cluster into two layers: The high-level region is indicated as ball and stick representation and the low-level region as tube rendering.

## Tables

Modified Mulliken charge analysis for orthosilicic acid with 75% and 100% of the electron overlap populations assigned to oxygen in a O–Si bond. Also shown are the regular Mulliken analysis (50% of the electron populations assigned to each O and Si), NBO, ESP derived charges, and Bader charges. The calculations are at the B3LYP/6-31G level.

Modified Mulliken charge analysis for orthosilicic acid with 75% and 100% of the electron overlap populations assigned to oxygen in a O–Si bond. Also shown are the regular Mulliken analysis (50% of the electron populations assigned to each O and Si), NBO, ESP derived charges, and Bader charges. The calculations are at the B3LYP/6-31G level.

Modified Mulliken charge analysis for the siloxide anion with 75% and 100% of the electron overlap populations assigned to oxygen in a O–Si bond. Also shown are the regular Mulliken analysis (50% of the electron populations assigned to each O and Si), NBO, ESP derived charges, and Bader charges. The calculations are at the B3LYP/6-31G level.

Modified Mulliken charge analysis for the siloxide anion with 75% and 100% of the electron overlap populations assigned to oxygen in a O–Si bond. Also shown are the regular Mulliken analysis (50% of the electron populations assigned to each O and Si), NBO, ESP derived charges, and Bader charges. The calculations are at the B3LYP/6-31G level.

Proton affinity (kcal/mol) of the spherosiloxane cube anion calculated by ONIOM-ME and ONIOM-EE. Also included for comparison are the target high-level and low-level methods. The mean absolute deviations of the ONIOM-ME and ONIOM-EE methods are 5.3 and , respectively.

Proton affinity (kcal/mol) of the spherosiloxane cube anion calculated by ONIOM-ME and ONIOM-EE. Also included for comparison are the target high-level and low-level methods. The mean absolute deviations of the ONIOM-ME and ONIOM-EE methods are 5.3 and , respectively.

Errors in the proton affinity of the spherosiloxane cube anion (model A) calculated by ONIOM-ME and ONIOM-EE with regular Mulliken point charges (50-50) and asymmetric Mulliken charges obtained by dividing the electron overlap populations between O and Si unequally as 60% on O, 40% on Si and 70% on O, 30% on Si.

Errors in the proton affinity of the spherosiloxane cube anion (model A) calculated by ONIOM-ME and ONIOM-EE with regular Mulliken point charges (50-50) and asymmetric Mulliken charges obtained by dividing the electron overlap populations between O and Si unequally as 60% on O, 40% on Si and 70% on O, 30% on Si.

Geometrical parameters for the hydroxylated spherosiloxane cube of symmetry, (model A) for various model chemistry combinations including ONIOM-ME and ONIOM-EE.

Geometrical parameters for the hydroxylated spherosiloxane cube of symmetry, (model A) for various model chemistry combinations including ONIOM-ME and ONIOM-EE.

Geometrical parameters for the deprotonated hydroxylated spherosiloxane anion of symmetry, (model A) for various model chemistry combinations including ONIOM-ME and ONIOM-EE.

Geometrical parameters for the deprotonated hydroxylated spherosiloxane anion of symmetry, (model A) for various model chemistry combinations including ONIOM-ME and ONIOM-EE.

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