### Abstract

Molecular structures are characterized by a large degree of additivity and transferability of various intramolecular interactions determining the shape and energetics of molecules. This property is constantly utilized by the different "molecular mechanics" (MM) schemes which allow one to obtain quite reliable molecular geometries and relative energy values for a wide range of molecular systems, which is especially remarkabke in the light of the simplicity of the assumptions made. Numerous MM schemes presented in the literature use different sets of parameters (force fields, etc.), which are adjusted empirically. The known success of MM models poses two important questions: first, one wishes to understand why do they work at all, and, second, one would like to develop schemes, in which the parameters of MM can be determined theoretically. Such an analysis could also give some deeper insight permitting to predict whether the given MM scheme is expected to be successful if applied to the class of problems actually at hand. From a more pragmatic point of view, having a bridge connecting a quantum mechanical (QM) description of molecular structure with a classical moldel (MM) can help to improve hybrid QM/MM methods by providing a systematic derivation of the form of the junction between the subsystems treated by MM and QM, respectively and by giving a priori estimates of the junction parameters. Our previous studies based on the semiempirical quantum chemical Hamiltonians of MINDO and MNDO types permitted us to draw the conclusion that the success of MM can indeed be understood on the basis of quantum mechanics. The analysis of the geminal-type wave functions constructed by making use of oriented hybrid orbitais showed that the parameters of the wave function and the energy contributions of the individual bonds are indeed well transferable, in good agreement with the simple chemical picture of the systems studied. It seems to be desirable to develop a similar analysis also at the ab initio level of the theory, because that would connect together the chemical and physical description of molecules and explain the observed transferability of molecular interactions more rigorously than semiempirical theories can do it. On the other hand this treatment might be also useful for developing QM/MM junctions in the cases when the QM part of the systems are described at the ab initio level. We report here results of the first step of this analysis: the geminal parameters expressed in a symmetrically orthogonalized optimized minimal basis set exhibit a degree of stability similar to that observed in the semiempirical case.

Original language | English |
---|---|

Pages (from-to) | 2539-2555 |

Number of pages | 17 |

Journal | International Journal of Quantum Chemistry |

Volume | 107 |

Issue number | 13 |

DOIs | |

Publication status | Published - Nov 5 2007 |

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### Keywords

- Additive schemes
- Molecular mechanics
- Quantum chemistry ab initio

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*International Journal of Quantum Chemistry*,

*107*(13), 2539-2555. https://doi.org/10.1002/qua.21454

**Towards a possible ab initio molecular mechanics. Transferability of density matrix elements.** / Tchougréeff, A. L.; Tokmachev, A. M.; Mayer, I.

Research output: Contribution to journal › Article

*International Journal of Quantum Chemistry*, vol. 107, no. 13, pp. 2539-2555. https://doi.org/10.1002/qua.21454

}

TY - JOUR

T1 - Towards a possible ab initio molecular mechanics. Transferability of density matrix elements

AU - Tchougréeff, A. L.

AU - Tokmachev, A. M.

AU - Mayer, I.

PY - 2007/11/5

Y1 - 2007/11/5

N2 - Molecular structures are characterized by a large degree of additivity and transferability of various intramolecular interactions determining the shape and energetics of molecules. This property is constantly utilized by the different "molecular mechanics" (MM) schemes which allow one to obtain quite reliable molecular geometries and relative energy values for a wide range of molecular systems, which is especially remarkabke in the light of the simplicity of the assumptions made. Numerous MM schemes presented in the literature use different sets of parameters (force fields, etc.), which are adjusted empirically. The known success of MM models poses two important questions: first, one wishes to understand why do they work at all, and, second, one would like to develop schemes, in which the parameters of MM can be determined theoretically. Such an analysis could also give some deeper insight permitting to predict whether the given MM scheme is expected to be successful if applied to the class of problems actually at hand. From a more pragmatic point of view, having a bridge connecting a quantum mechanical (QM) description of molecular structure with a classical moldel (MM) can help to improve hybrid QM/MM methods by providing a systematic derivation of the form of the junction between the subsystems treated by MM and QM, respectively and by giving a priori estimates of the junction parameters. Our previous studies based on the semiempirical quantum chemical Hamiltonians of MINDO and MNDO types permitted us to draw the conclusion that the success of MM can indeed be understood on the basis of quantum mechanics. The analysis of the geminal-type wave functions constructed by making use of oriented hybrid orbitais showed that the parameters of the wave function and the energy contributions of the individual bonds are indeed well transferable, in good agreement with the simple chemical picture of the systems studied. It seems to be desirable to develop a similar analysis also at the ab initio level of the theory, because that would connect together the chemical and physical description of molecules and explain the observed transferability of molecular interactions more rigorously than semiempirical theories can do it. On the other hand this treatment might be also useful for developing QM/MM junctions in the cases when the QM part of the systems are described at the ab initio level. We report here results of the first step of this analysis: the geminal parameters expressed in a symmetrically orthogonalized optimized minimal basis set exhibit a degree of stability similar to that observed in the semiempirical case.

AB - Molecular structures are characterized by a large degree of additivity and transferability of various intramolecular interactions determining the shape and energetics of molecules. This property is constantly utilized by the different "molecular mechanics" (MM) schemes which allow one to obtain quite reliable molecular geometries and relative energy values for a wide range of molecular systems, which is especially remarkabke in the light of the simplicity of the assumptions made. Numerous MM schemes presented in the literature use different sets of parameters (force fields, etc.), which are adjusted empirically. The known success of MM models poses two important questions: first, one wishes to understand why do they work at all, and, second, one would like to develop schemes, in which the parameters of MM can be determined theoretically. Such an analysis could also give some deeper insight permitting to predict whether the given MM scheme is expected to be successful if applied to the class of problems actually at hand. From a more pragmatic point of view, having a bridge connecting a quantum mechanical (QM) description of molecular structure with a classical moldel (MM) can help to improve hybrid QM/MM methods by providing a systematic derivation of the form of the junction between the subsystems treated by MM and QM, respectively and by giving a priori estimates of the junction parameters. Our previous studies based on the semiempirical quantum chemical Hamiltonians of MINDO and MNDO types permitted us to draw the conclusion that the success of MM can indeed be understood on the basis of quantum mechanics. The analysis of the geminal-type wave functions constructed by making use of oriented hybrid orbitais showed that the parameters of the wave function and the energy contributions of the individual bonds are indeed well transferable, in good agreement with the simple chemical picture of the systems studied. It seems to be desirable to develop a similar analysis also at the ab initio level of the theory, because that would connect together the chemical and physical description of molecules and explain the observed transferability of molecular interactions more rigorously than semiempirical theories can do it. On the other hand this treatment might be also useful for developing QM/MM junctions in the cases when the QM part of the systems are described at the ab initio level. We report here results of the first step of this analysis: the geminal parameters expressed in a symmetrically orthogonalized optimized minimal basis set exhibit a degree of stability similar to that observed in the semiempirical case.

KW - Additive schemes

KW - Molecular mechanics

KW - Quantum chemistry ab initio

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U2 - 10.1002/qua.21454

DO - 10.1002/qua.21454

M3 - Article

AN - SCOPUS:34548564283

VL - 107

SP - 2539

EP - 2555

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 13

ER -