Research

 

· Efficient molecular mechanics for chemical reactions:  multi-configuration molecular mechanics (MCMM) using partial electronic structure Hessians

The MCMM method (see Fig.1) is an extension of standard molecular mechanics (MM) for chemical reactions through interacting valence-bonding configurations. This is achieved by description of the reactant and product by MM potential energy functions and by incorporation of quantum mechanical effects into the resonance between the reactant and product configurations. MCMM differs from other methods that also use diabatic representation of the Hamiltonian in two aspects:

1.      Calibration of the resonance between valence-bonding configurations to the quantum mechanical calculations.

2.      Use of a very general interpolation scheme to generate a semi-global potential energy surface (PES) in a multi-dimensional space, which covers kinetically important regions for a reaction ¾ regions along the reaction path and also at the concaved side that is critical for large curvature tunneling.

 

Fig 1. In MCMM, the actual representation for a molecular is obtained through two interacting (reactant and product) MM configurations. The resonance energy describes the interaction between the reactant and product configurations of different bonding patterns, and with the QM contributions built in.

Fig. 2. Schematics for the potential energy surface, sample trajectory, location of generalized transition state, and multi-dimensional tunneling path.

 

Recently we demonstrated that the efficiency of the MCMM method can be significantly improved by reducing (up to an order of magnitude) the computational costs associated with the Hessian determinations for involved non-stationary geometries. Such Hessian calculations often dominate the computational efforts for the standard MCMM strategy. The improvement is achieved by use of electronic structure calculations only for certain critical elements of the Hessians at the non-stationary points and by use of interpolation for the other elements at the non-stationary points.

 

This new MCMM strategy was tested by the variational transition state theory with multi-dimensional tunneling (VTST/MT) for a diverse test suite of six reactions involving hydrogen-atom transfer. The VTST/MT theory optimizes the location of the generalized transition state, and it also includes contributions due to multi-dimensional tunneling, as depicted in Fig. 2. The new MCMM method yields quite accurate rate constants. The saving on computational efforts by this new procedure makes MCMM more affordable for fitting expensive electronic structure methods applied to medium-size molecules and also makes a promising step toward application of MCMM to very large molecules.

 

· Charge redistribution for link atoms in combined quantum-mechanics/molecular-mechanics (QM/MM)

The combined quantum mechanics and molecular mechanics (QM/MM) method (see Fig. 3) is a powerful tool for studying large reactive systems. A QM/MM model treats a relatively localized region (e.g., where bond breaking/forming or electronic excitation occur) with QM methods and includes the influence of the surroundings at the MM level. QM/MM provides a realistic description and also a computationally feasible tool for the system to study.

Fig. 3. Illustration for the QM/MM method in the enzyme system. The active site is treated at the QM level and the surroundings is treated at the  MM level. In contrast to isolated-model calculations, QM/MM method considers the effects due to protein environment on the active center.

 

Special treatments are needed to take care of the QM/MM boundary when the QM and MM separation goes through a covalent bond. Such treatments can be largely grouped into two classes: the link-atom method and the local-orbital method. The link-atom method uses one-free-valence atoms such as hydrogen atoms to saturate the dangling bonds of the QM fragments. The local-orbital method is a mixed molecular-orbital valence-orbital calculation, where the QM/MM boundary is described by a set of local hybrid orbitals. The generalized hybrid orbital (GHO) theory is one of the local orbital approaches. In general, the link atom method is simple and straightforward but the frozen orbital method is more theoretically fundamental.

Fig. 4. The redistributed charge scheme (lower panel) is an classic analog to the quantum description by the generalized hybrid orbital (GHO) theory. The MM boundary atom and the active hybrid orbital (shown in red) in the GHO theory are now modeled by an H atom, and the auxiliary orbitals (shown in blue) are modeled by three point charges.

 

 

Recently, we developed the charge redistribution scheme for link atoms, which combines the simplicity of the link atom and solid theoretical justification of local-orbital methods. The charge redistribution scheme uses redistributed point charges as mimics to the frozen auxiliary hybrid orbitals in the GHO theory (see Fig. 4). The charge redistribution scheme offer the following advantages:

  1. The way it handles the MM point charges near the QM/MM boundary is justified by a classical analog to the QM description.
  2. Its simplicity allows direct incorporation into most electronic structure programs in a general way.

Reasonably good results have been obtained by the charge redistribution scheme as demonstrated by a series of tests calculations including computations for geometries, energies, and vibrational frequencies, in comparison with full QM calculations. This shows that the charge redistribution scheme provides a reasonable and practical way to treat the QM/MM boundary. 

 

· Cytochrome P450 enzymes by combined quantum-mechanical/molecular mechanical (QM/MM) calculations

The bacterial enzyme cytochrome P450cam catalyses the highly regio- and stereo-selective hydroxylation of a C-H bond of its natural substrate, camphor (see Fig. 5). However, there are debates on the electronic nature of the active oxidant and on the mechanism of the reaction. Previous calculations in gas phase yielded model-dependent conclusions. This situation motivated our studies on this enzyme employing QM/MM method. In our investigation, the QM subsystems including parts of the heme, camphor, and proximal cysteine were treated with density functional theory, whereas the surrounding enzyme and solvent were modeled with a classical force field. The QM/MM computations were compared with pure QM model calculations in gas phase.

 

Fig. 5. The active center for P450cam, which catalyzes hydroxylation of camphor to form 5-exo-hydroxycamphor.

 

1.       Electronic nature of the active oxidant Compound I. We found that the presence of H-bond donors, the polarizing effect of the enzyme matrix, and the steric constraints of the protein pocket act simultaneously. The most striking finding is that Compound I is shown to be transformed by the protein environment from a sulfur-centered radical to the green 2,4A2u porphyrin-centered radical cation, in excellent agreement with experiments. This leads to the conclusion that Compound I thus behaves as a chameleon species that adapts its electronic and structural character to the specific environment.

 

  1. Hydroxylation of the C5-H(5-exo) bond in camphor. The calculated energy profile of the hydrogen-abstraction oxygen-rebound mechanism indicates that the reaction takes place in two spin states (doublet and quartet), as has been suggested earlier on the basis of calculations on simpler models (“two-state-reactivity”). While the reaction on the doublet potential energy surface is non-synchronous, yet effectively concerted, the quartet pathway is truly stepwise, including formation of a distinct intermediate substrate radical and a hydroxo-iron complex. The dynamical coupling between these two spin states provides a satisfactory explanation for seemingly contradictory experimental findings, which on one hand suggested the presence of radical intermediates, but on the other hand yielded unreasonably short lifetimes for these intermediates.

 

3.      The enzyme-product complex in the catalytic cycle. Computations indicate a doublet minimum at a Fe-O distance of ca. 2.2 Å, and a flat, barrierless potential for the dissociation of the Fe-O bond. The protein environment (i) facilitates the cleavage of the Fe-O bond by favorable interactions of hydroxycamphor with the binding pocket, and (ii) lowers the quartet and sextet states relative to the doublet, which has consequences for the intersection points of the spin surfaces. The calculations are consistent with detailed low temperature electron nuclear double resonance (ENDOR) studies at 200 K.

In conclusion, the QM/MM studies have demonstrated the importance of the protein environment for a correct theoretical description of an enzymatic reaction and also the capability of QM/MM calculations to evaluate the properties of an active species in its actual protein environment.

 

·  Vibrational overtones via theoretical potential energy and dipole moment surfaces

Studies of energies and intensities of vibrational overtones are essential for understanding molecular reaction dynamics. High-level quantum-chemical calculations are complementary to experiments in this area. We have performed a systematic investigation of the overtones, especially on the intensities, for a series of molecules using ab initio potential energy surfaces (PES) and dipole moment surfaces (DMS). Examples include:

  1. A highly accurate semi-global full-dimensional PES was constructed to describe the large amplitude inversion motion in NH3, for which core-valence correlation and relativistic corrections are considered. Variational calculations based on this PES yield energy levels and intensity patterns in excellent agreement with experimental data.

Fig. 6. Comparison of calculated and observed relative intensities for the vibrational overtones for CHCl3.

Fig. 7. Overlap integrals between excited-state wavefunctions and the dipole-weighted-ground-state wavefunction, which is defined as the product of the dipole function and the ground-state wavefunction.

2.      The first overtone of the C-H stretching mode is experimentally found to be stronger than the corresponding fundamental in CHCl3. This anomaly was rationalized employing dipole-weighted overlap integrals, demonstrating the importance of electric anharmonicity

In conclusion, the energy and intensity patterns are well reproduced for these species. In particular we have deepened the insight into the intensities associated with the vibrational excitations.

 

·        Reactions for Organic Species in the Atmosphere

The presence of organic trace gas species in atmosphere has significant influence on our environments. An example is CH4, which contributes to global warming as an important greenhouse species due to its large abundance in atmosphere and its intense adsorption in the infrared region. The reaction of OH with CH4 controls the balance of O3, which protects lives on the earth by adsorption of the ultraviolet radiations. The atmospheric concentrations of CH4 and of non-methane organic compounds (NMOCs) are of great importance to the global climate changes and environment protection. Atmospheric simulations have been performed to quantify the sources and sinks for these species whose atmospheric kinetic isotopic composition are used as a constraint. It has been found that the success in such a modeling depends on how accurately we know the kinetic isotope effects (KIEs) and their temperature dependence for the reactions responsible for the destruction of these compounds.

The importance of the reactions of OH with CH4 and NMOCs stimulates a large number of experimental and theoretical investigations, and significant progress has been made in past decades in elucidation of the reaction mechanics and in quantification of the KIEs. However, many problems remain unsolved, even for the reaction of OH with CH4, one of the most extensively studied cases. For example, the 13C KIE and its temperature dependence for this reaction have not yet been measured in the whole temperature range of importance to atmospheric science, while theoretical calculations addressing this problem have predicted even qualitatively different temperature dependences.

Fig. 8. Illustration for the harmonic and torsional energy curves for the torsional mode at the saddle point for reaction OH + CH4 à H2O + CH3, as well as the kBT at the 225 and 296 K.

We probed the KIE and its temperature dependence for the reactions of OH with CH4.

(1)   We employed the variational transition state theory with multi-dimensional tunneling treatments, and we compared the results with those obtained by the conventional transition state theory with one-dimensional tunneling treatments using the same potential energy surfaces. This comparison will reveal the changes due to improvement in dynamical theory, e.g., the effects due to the coupling between the motions in the reaction coordinate and in the transverse normal modes. Such couplings are included in the multi-dimensional tunneling treatments but excluded in the one-dimensional tunneling treatments.

(2)   We explored the potential anharmonicity and its effects on the KIEs. A large-amplitude vibration, e.g., a torsional motion, shows prominent deviations from the harmonic potential energy curve (Fig. 8). The partition function for such kind of a mode is likely to be incorrectly evaluated by use of the harmonic approximation, and should be handled in an appropriate treatment. We demonstrated that the variational effects and multi-dimensional tunneling contributions change the “unusual” 13C KIE temperature dependence predicted by TST and one-dimensional tunneling treatments to a “normal” one, and the potential anharmonicity is crucial to the magnitude of the 13C KIE value.

 

 

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Several years ago, I was doing experiments … J

 

·  Fourier transform intra-cavity laser absorption spectroscopy

We have developed the Fourier transform intra-cavity laser absorption (FT-ICLA) spectrometry by combining a rapid scan FT spectrometer with a standing wave titanium sapphire laser. This novel technique integrates the high-resolution and high-accuracy merits of the Fourier transform spectroscopy and the high-sensitivity nature of the intra-cavity laser absorption spectroscopy. Application to the study of HOD overtones demonstrated that it is an ideal apparatus for weak absorption detection.

 

·  Scanning tunneling microscopy and single atom (molecule) manipulation

There has been a growing interest in the possibility of observing and manipulating chemical events at the single molecular scale. During my early academic career, I have been involved in such experiments, especially in STM measurements of the adsorption sites of individual C60 molecules on Si(111)7´7 surface. The obtained C60 adsorption orientation and intra-molecular structure patterns agree well with theoretical predictions.