Generalized Hybrid Orbital Method Research Articles

QM/MM calculation of protein magnetic shielding tensors with generalized hybrid-orbital method: A GIAO approach

A method to compute magnetic shielding tensors with generalized hybrid-orbital (GHO) QM/MM scheme is developed at the levels of Hartree-Fock and second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals. A feature of the GHO method is utilized to ensure gauge-origin independency of GHO shielding tensors in a simple way. The benchmark calculations indicate that the GHO method reproduced full-QM shielding constants nearly quantitatively for atoms not directly coupled to the GHO linking atoms. As an application to a realistic protein, carbon chemical shifts are calculated for the retinal chromophore in visual rhodopsin.

Simple avoidance of Pauli repulsion errors in the generalized hybrid orbital (GHO) method

We assess transformation matrices in the combined quantum mechanical and molecular mechanical method based on generalized hybrid orbitals (GHO). In addition to the previous ones, we examine a restrained transformation matrix based on the assumption that all coefficients of the p-hybridized orbitals are uniform and each hybridized orbital points toward a vertex of a tetrahedron. It is clearly shown that the new implementation improves the accuracy of the GHO method reducing the error concerning the Pauli repulsion about auxiliary orbitals.

Improvements in the generalized hybrid orbital method

AbstractIn a previous paper, we described the adaptation of the generalized hybrid orbital (GHO) method for the use in fragment based quantum chemical approaches for large molecules like the field‐adapted adjustable density matrix assembler (FA‐ADMA). It soon became evident that the limitations of the available implementation strongly restrict its use. Therefore, in the article presented here, we describe new developments to circumvent these limitations. These include new construction algorithms of the GHO hybrid orbitals for sp3‐ as well as sp2‐hybridized carbon and nitrogen, different distributions of electrons in the auxiliary orbitals, and the separation from the CHARMM program, which was needed to provide partial charges and bonding information. The results demonstrate an excellent improvement in accuracy of the obtained electron densities compared to capping hydrogen atoms. Additionally, the calculation of gradients opens the possibility to use FA‐ADMA for geometry optimization of large molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

New implementation of a combined quantum mechanical and molecular mechanical method using modified generalized hybrid orbitals

Two new techniques are introduced in the generalized hybrid orbital (GHO) method [Pu et al., J. Phys. Chem. A 108, 632 (2004)] and tested on small molecules. The first is a way to determine occupation numbers dependent on the molecular mechanical (MM) atoms linked to the boundary. The method takes account of the inhomogeneity in the occupation numbers of the auxiliary orbitals from different types of MM atoms in such a way that the formal charge condition is fulfilled. The second technique is a rigorous orthogonalization procedure of auxiliary orbitals for more than two boundary atoms. It is shown that the new implementation widens the realm of the GHO method with flexible quantum mechanical/MM partitionings.

Generalized Hybrid‐Orbital Method for Combining Density Functional Theory with Molecular Mechanicals

The generalized hybrid orbital (GHO) method has previously been formulated for combining molecular mechanics with various levels of quantum mechanics, in particular semiempirical neglect of diatomic differential overlap theory, ab initio Hartree-Fock theory, and self-consistent charge density functional tight-binding theory. To include electron-correlation effects accurately and efficiently in GHO calculations, we extend the GHO method to density functional theory in the generalized-gradient approximation and hybrid density functional theory (denoted by GHO-DFT and GHO-HDFT, respectively) using Gaussian-type orbitals as basis functions. In the proposed GHO-(H)DFT formalism, charge densities in auxiliary hybrid orbitals are included to calculate the total electron density. The orthonormality constraints involving the auxiliary Kohn-Sham orbitals are satisfied by carrying out the hybridization in terms of a set of Löwdin symmetrically orthogonalized atomic basis functions. Analytical gradients are formulated for GHO-(H)DFT by incorporating additional forces associated with GHO basis transformations. Scaling parameters are introduced for some of the one-electron integrals and are optimized to obtain the correct charges and geometry near the QM/MM boundary region. The GHO-(H)DFT method based on the generalized gradient approach (GGA) (BLYP and mPWPW91) and HDFT methods (B3 LYP, mPW1PW91, and MPW1 K) is tested-for geometries and atomic charges-against a set of small molecules. The following quantities are tested: 1) the C--C stretch potential in ethane, 2) the torsional barrier for internal rotation around the central C--C bond in n-butane, 3) proton affinities for a set of alcohols, amines, thiols, and acids, 4) the conformational energies of alanine dipeptide, and 5) the barrier height of the hydrogen-atom transfer between n-C4H10 and n-C4H9, where the reaction center is described at the MPW1 K/6-31G(d) level of theory.

Redistributed Charge and Dipole Schemes for Combined Quantum Mechanical and Molecular Mechanical Calculations

Special care is needed in carrying out combined quantum mechanical and molecular mechanical (QM/MM) calculations if the QM/MM boundary passes through a covalent bond. The present paper discusses the importance of correctly handling the MM partial point charges at the QM/MM boundary, and in particular, it contributes in two aspects: (1) Two schemes, namely, the redistributed charge (RC) scheme and the redistributed charge and dipole (RCD) scheme, are introduced to handle link atoms in QM/MM calculations. In both schemes, the point charge at the MM boundary atom that is replaced by the link atom is redistributed to the midpoint of the bonds that connect the MM boundary atom and its neighboring MM atoms. These redistributed charges serve as classical mimics for the auxiliary orbitals associated with the MM host atom in the generalized hybrid orbital (GHO) method. In the RCD scheme, the dipoles of these bonds are preserved by further adjustment of the values of the redistributed charges. The treatments are justified as classical analogues of the QM description given by the GHO method. (2) The new methods are compared quantitatively to similar methods that were suggested by previous work, namely, a shifted-charge scheme and three eliminated-charge schemes. The comparisons were carried out for a series of molecules in terms of proton affinities and geometries. Point charges derived from various charge models were tested. The results demonstrate that it is critical to preserve charge and bond dipole and that it is important to use accurate MM point charges in QM/MM boundary treatments. The RCD scheme was further applied to study the H atom transfer reaction CH3 + CH3CH2CH2OH --> CH4 + CH2CH2CH2OH. Various QM levels of theory were tested to demonstrate the generality of the methodology. It is encouraging to find that the QM/MM calculations obtained a reaction energy, barrier height, saddle-point geometry, and imaginary frequency at the saddle point in quite good agreement with full QM calculations at the same level. Furthermore, analysis based on energy decomposition revealed the quantitatively similar interaction energies between the QM and the MM subsystems for the reactant, for the saddle point, and for the product. These interaction energies almost cancel each other energetically, resulting in negligibly small net effects on the reaction energy and barrier height. However, the charge distribution of the QM atoms is greatly affected by the polarization effect of the MM point charges. The QM/MM charge distribution agrees much better with full QM results than does the unpolarized charge distribution of the capped primary subsystem.

Combining Self-Consistent-Charge Density-Functional Tight-Binding (SCC-DFTB) with Molecular Mechanics by the Generalized Hybrid Orbital (GHO) Method

In combined quantum mechanical and molecular mechanical (QM/MM) calculations with the QM/MM boundary at a covalent bond, the generalized hybrid orbital (GHO) method has been shown to provide a well balanced and stable connection between the QM and MM regions. The GHO method has previously been developed for semiempirical molecular orbital methods based on neglect of diatomic differential overlap (GHO-NDDO) and for the ab initio Hartree-Fock level (GHO-AIHF). In the present work, we formulate the GHO algorithm and its analytical gradients for treating the QM subsystem by the self-consistent-charge densityfunctional tight-binding (SCC-DFTB) theory. To obtain a good description of the bond length at the QM/ MM boundary, a parametrized empirical correction term involving the GHO boundary atom and its QM frontier neighbor is added. Geometries and Mulliken charges obtained from GHO-SCC-DFTB calculations are compared to the fully QM results for a set of 18 molecules and ions with various functional groups close to the boundary, and we verified that we reproduced the full C-C stretch potential in ethane and in propanoate. The torsion barrier of n-butane around the central C-C bond is studied with the GHO boundary atom placed at different locations. Finally, the energetics of the method are tested for the proton affinities of a series of 15 alcohols, amines, thiols, and acids. The results indicate that the GHO treatment for combining SCCDFTB with molecular mechanics is both theoretically robust and satisfactory for practical use. In Supporting Information we present parameters for boundaries that cut through O-C and S-C bonds.

Generalized Hybrid Orbital (GHO) Method for Combining Ab Initio Hartree−Fock Wave Functions with Molecular Mechanics

The generalized hybrid orbital (GHO) method provides a way to combine quantum mechanical (QM) and molecular mechanical (MM) calculations on a single molecular system or supramolecular assembly by providing an electrostatically stable connection between the QM portion and the MM portion. The GHO method has previously been developed for semiempirical molecular orbital calculations, on the basis of neglect of diatomic differential overlap (GHO−NDDO); in the present work, it is extended to the ab initio Hartree−Fock (HF) level (GHO−AIHF). First, the theoretical foundation for the GHO−AIHF extension is discussed, and four different approaches are proposed to overcome the nonorthogonality between active molecular orbitals (MOs) and auxiliary MOs. In the first scheme, the auxiliary hybrid basis functions are projected out of the active QM basis. The second scheme neglects the diatomic differential overlap between the auxiliary basis and the active QM basis. In the third scheme, hybrid orbitals are constructed fr...

Generalized hybrid orbital for the treatment of boundary atoms in combined quantum mechanical and molecular mechanical calculations using the semiempirical parameterized model 3 method

The application of combined quantum mechanical (QM) and molecular mechanical methods to large molecular systems requires an adequate treatment of the boundary between the two approaches. In this article, we extend the generalized hybrid orbital (GHO) method to the semiempirical parameterized model 3 (PM3) Hamiltonian combined with the CHARMM force field. The GHO method makes use of four hybrid orbitals, one of which is included in the QM region in self-consistent field optimization and three are treated as auxiliary orbitals that do not participate in the QM optimization, but they provide an effective electric field for interactions. An important feature of the GHO method is that the semiempirical parameters for the boundary atom are transferable, and these parameters have been developed for a carbon boundary atom consistent with the PM3 model. The combined GHO-PM3/CHARMM model has been tested on molecular geometry and proton affinity for a series of organic compounds.

The generalized hybrid orbital method for combined quantum mechanical/molecular mechanical calculations: formulation and tests of the analytical derivatives

Hybrid quantum mechanical (QM) and molecular mechanical (MM) potentials are becoming increasingly important for studying condensed-phase systems but one of the outstanding problems in the field has been how to treat covalent bonds between atoms of the QM and MM regions. Recently, we presented a generalized hybrid orbital (GHO) method that was designed to tackle this problem for hybrid potentials using semiempirical QM methods [Gao et al. (1998) J Phys Chem A 102: 4714–4721]. We tested the method on some small molecules and showed that it performed well when compared to the purely QM or MM potentials. In this article, we describe the formalism for the determination of the GHO energy derivatives and then present the results of more tests aimed at validating the model. These tests, involving the calculation of the proton affinities of some model compounds and a molecular dynamics simulation of a protein, indicate that the GHO method will prove useful for the application of hybrid potentials to solution-phase macromolecular systems.

A Generalized Hybrid Orbital (GHO) Method for the Treatment of Boundary Atoms in Combined QM/MM Calculations

A generalized hybrid orbital (GHO) method has been developed at the semiempirical level in combined quantum mechanical and molecular mechanical (QM/MM) calculations. In this method, a set of hybrid orbitals is placed on the boundary atom between the QM and MM fragments, and one of the hybrid orbitals participates in the SCF calculation for the atoms in the QM region. The GHO method provides a well-defined potential energy surface for a hybrid QM/MM system and is a significant improvement over the “link-atom” approach by saturating the QM valencies with hydrogen atoms. The method has been tested on small molecules and yields reasonable structural, energetic, and electronic results in comparison with the results of the corresponding QM and MM approximations. The GHO method will greatly increase the applicability of combined QM/MM methods to systems comprising large molecules, such as proteins.