6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

/pdf/quantum-mechanical-continuum-solvation-models-3edv963g14.pdf

Quantum mechanical continuum solvation models.

There are now a wide variety of packages for electronic structure calculations, each of which differs in the algorithms implemented and the output format. Many computational chemistry algorithms are only available to users of a particular package despite being generally applicable to the results of calculations by any package. Here we present cclib, a platform for the development of package-independent computational chemistry algorithms. Files from several versions of multiple electronic structure packages are automatically detected, parsed, and the extracted information converted to a standard internal representation. A number of population analysis algorithms have been implemented as a proof of principle. In addition, cclib is currently used as an input filter for two GUI applications that analyze output files: PyMOlyze and GaussSum. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008

cclib: A library for package‐independent computational chemistry algorithms

Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.

QM/MM Methods for Biomolecular Systems

Based on its generally accessible I/II redox couple and bioavailability, copper plays a wide variety of roles in nature that mostly involve electron transfer (ET), O2 binding, activation and reduction, NO2− and N2O reduction and substrate activation. Copper sites that perform ET are the mononuclear blue Cu site that has a highly covalent CuII-S(Cys) bond and the binuclear CuA site that has a Cu2S(Cys)2 core with a Cu-Cu bond that keeps the site delocalized (Cu(1.5)2) in its oxidized state. In contrast to inorganic Cu complexes, these metalloprotein sites transfer electrons rapidly often over long distances, as has been previously reviewed.1–4 Blue Cu and CuA sites will only be considered here in their relation to intramolecular ET in multi-center enzymes. The focus of this review is on the Cu enzymes (Figure 1). Many are involved in O2 activation and reduction, which has mostly been thought to involve at least two electrons to overcome spin forbiddenness and the low potential of the one electron reduction to superoxide (Figure 2).5,6 Since the Cu(III) redox state has not been observed in biology, this requires either more than one Cu center or one copper and an additional redox active organic cofactor. The latter is formed in a biogenesis reaction of a residue (Tyr) that is also Cu catalyzed in the first turnover of the protein. Recently, however, there have been a number of enzymes suggested to utilize one Cu to activate O2 by 1e− reduction to form a Cu(II)-O2•− intermediate (an innersphere redox process) and it is important to understand the active site requirements to drive this reaction. The oxidases that catalyze the 4e−reduction of O2 to H2O are unique in that they effectively perform this reaction in one step indicating that the free energy barrier for the second two-electron reduction of the peroxide product of the first two-electron step is very low. In nature this requires either a trinuclear Cu cluster (in the multicopper oxidases) or a Cu/Tyr/Heme Fe cluster (in the cytochrome oxidases). The former accomplishes this with almost no overpotential maximizing its ability to oxidize substrates and its utility in biofuel cells, while the latter class of enzymes uses the excess energy to pump protons for ATP synthesis. In bacterial denitrification, a mononuclear Cu center catalyzes the 1e- reduction of nitrite to NO while a unique µ4S2−Cu4 cluster catalyzes the reduction of N2O to N2 and H2O, a 2e− process yet requiring 4Cu’s. Finally there are now several classes of enzymes that utilize an oxidized Cu(II) center to activate a covalently bound substrate to react with O2.



Figure 1

Copper active sites in biology.





Figure 2

Latimer Diagram for Oxygen Reduction at pH = 7.0 Adapted from References 5 and 6.



This review presents in depth discussions of all these classes of Cu enzymes and the correlations within and among these classes. For each class we review our present understanding of the enzymology, kinetics, geometric structures, electronic structures and the reaction mechanisms these have elucidated. While the emphasis here is on the enzymology, model studies have significantly contributed to our understanding of O2 activation by a number of Cu enzymes and are included in appropriate subsections of this review. In general we will consider how the covalency of a Cu(II)–substrate bond can activate the substrate for its spin forbidden reaction with O2, how in binuclear Cu enzymes the exchange coupling between Cu’s overcomes the spin forbiddenness of O2 binding and controls electron transfer to O2 to direct catalysis either to perform two e− electrophilic aromatic substitution or 1e− H-atom abstraction, the type of oxygen intermediate that is required for H-atom abstraction from the strong C-H bond of methane (104 kcal/mol) and how the trinuclear Cu cluster and the Cu/Tyr/Heme Fe cluster achieve their very low barriers for the reductive cleavage of the O-O bond.

Much of the insight available into these mechanisms in Cu biochemistry has come from the application of a wide range of spectroscopies and the correlation of spectroscopic results to electronic structure calculations. Thus we start with a tutorial on the different spectroscopic methods utilized to study mononuclear and multinuclear Cu enzymes and their correlations to different levels of electronic structure calculations.

/pdf/copper-active-sites-in-biology-lhhabv47if.pdf

Copper Active Sites in Biology

Vibrational Energy Distribution Analysis (VEDA): Scopes and limitations

Gaussian 03, Revision E.01.

Gaussian 09W, revision A. 02

Geometry optimization of large QM/MM systems is usually carried out by alternating a second-order optimization of the QM region using internal coordinates (‘macro-iterations’), and a first-order optimization of the MM region using Cartesian coordinates (‘micro-iterations’), until self-consistency. However, the neglect of explicit coupling between the two regions (the Hessian elements that couple the QM coordinates with the MM coordinates) often interferes with a smooth convergence, while the Hessian update procedure can be unstable due to the presence of multiple minima in the MM region. A new geometry optimization scheme for QM/MM methods is proposed that addresses these problems. This scheme explicitly includes the coupling between the two regions in the QM optimization step, which makes it quadratic in the full space of coordinates. Analytical second derivatives are used for the MM contributions, with O(N) memory and CPU requirements (where N is the total number of atoms) by employing direct and fast m...

Geometry optimization with QM/MM methods II: Explicit quadratic coupling

We report calculations of the optical rotations of six 6,8-dioxabicyclo[321]octanes using ab initio density functional theory (DFT) GIAO basis sets are used to ensure origin independence of predicted rotations Large basis sets including diffuse functions are used to minimize basis set error The signs of [ α ] D are correctly predicted Magnitudes differ from experiment by 10–20 degrees [dm (g/cc)] −1 on average Agreement with experiment is improved by inclusion of solvent effects via the polarized continuum model (PCM) The results support the conclusion that DFT/GIAO/PCM calculations of specific rotations can be useful in elucidating the absolute configurations of chiral molecules

Prediction of optical rotation using density functional theory: 6,8-dioxabicyclo[3.2.1]octanes

To highlight the role of the protein in metal enzyme catalysis, we optimize ONIOM QM:MM transition states and intermediates for the full reaction of the nonheme iron enzyme isopenicillin N synthase (IPNS). Optimizations of transition states in large protein systems are possible using our new geometry optimizer with quadratic coupling between the QM and MM regions [Vreven, T. et al. Mol. Phys. 2006, 104, 701−704]. To highlight the effect of the metal center, results from the protein model are compared to results from an active site model containing only the metal center and coordinating residues [Lundberg, M. et al. Biochemistry 2008, 47, 1031−1042]. The analysis suggests that the main catalytic effect comes from the metal center, while the protein controls the reactivity to achieve high product specificity. As an example, hydrophobic residues align the valine substrate radical in a favorable conformation for thiazolidine ring closure and contribute to product selectivity and high stereospecificity. A low-...

/pdf/transition-states-in-a-protein-environment-oniom-qm-mm-34dfqh4sg4.pdf

Michael J. Frisch

Papers

Gaussian 03, Revision E.01.

Gaussian 09W, revision A. 02

Geometry optimization with QM/MM methods II: Explicit quadratic coupling

Prediction of optical rotation using density functional theory: 6,8-dioxabicyclo[3.2.1]octanes

Transition States in a Protein Environment - ONIOM QM:MM Modeling of Isopenicillin N Synthesis.