The Generalized Hybrid Orbital (GHO) Method

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The GHO method was develeped in collaboration with Dr. Martin Field to treat the transition from the quantum mechanical region to the molecular mechanical region across covalent bonds in combined QM/MM calculations.  We partition the hybrid orbitals of the boundary atoms into "active" orbitals and auxiliary orbitals.  The hybrid active orbitals, along with the atomic orbital basis functions, are optimized in SCF calculations, whereas the charge density of the auxiliary orbitals acts as an effective potential for the boundary atoms.  There are a number of important features of the method, which are in contrast to the traditional hydrogen "link-atom" approach.  (1) The hybrid orbitals are defined by the local geometry of the boundary atom. Thus, dynamic fluctuation of the molecular structure allows re-hybridizations and bond polarization between the QM and MM region to be adequately represented.  (2) The boundary atom is considered both "quantum mechanical" and classical.  Optimization of the active hybrid orbitals in SCF calculations permits charge transfer between the QM fragment and the boundary atoms, which retain MM partial charges.  (3) There is no charge deleted, added, or modified in the MM region - all partial charges in the MM region, including the boundary atoms are retained.   Furthermore, all electrostatic interactions between QM and MM regions are included in the computation so that there is continuous transition of electrostatic properties.   (4) The system retains the same number of nuclear degrees of freedom as in pure MM or QM calculations.

The GHO method has been implemented in CHARMM version 28.

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Three criteria are important to assess methods to treat the QM/MM boundary:
  1. The geometry predicted by the QM/MM method must be in agreement with results from pure QM and MM calculations for the same set of model compounds.
  2. The electronic structure of the full QM system should be retained in the QM fragment with the introduction of boundary atoms and MM fragments.
  3. The conformational energies from hybrid QM/MM calculations should be comparable to energies for the QM and MM fragments individually.

The first criterion is met by adjusting the value of the semiempirical parameter for the resonance integral, H12 (beta), which in turn is uniquely defined by this requirement.

The second criterion limits the range of the core electron integral, Uss and Upp, and the need for no charge transfer in hydrocarbon compounds also uniquely defines these values.

The third criterion is naturally met by the GHO method - good agreement in predicted torsional energy profiles has been obtained from the QM and MM region.

 

Method: J. Gao, P. Amara, C. Alhambra, M. J. Field, J. Phys. Chem. A, 102, 4714 (1998).

Derivatives: P. Amara, M. J. Field, C. Alhambra, J. Gao, Theoret. Chem. Acc. in press.