Projected Hybrid Orbitals: A General QM/MM Method

A projected hybrid orbital (PHO) method was described to model the covalent boundary in a hybrid quantum mechanical and molecular mechanical (QM/MM) system. The PHO approach can be used in ab initio wave function theory and in density functional theory with any basis set without introducing system-dependent parameters. In this method, a secondary basis set on the boundary atom is introduced to formulate a set of hybrid atomic orbtials. The primary basis set on the boundary atom used for the QM subsystem is projected onto the secondary basis to yield a representation that provides a good approximation to the electron-withdrawing power of the primary basis set to balance electronic interactions between QM and MM subsystems. The PHO method has been tested on a range of molecules and properties. Comparison with results obtained from QM calculations on the entire system shows that the present PHO method is a robust and balanced QM/MM scheme that preserves the structural and electronic properties of the QM region

AM1/d-CB1: A Semiempirical Model for QM/MM Simulations of Chemical Glycobiology Systems

A semiempirical method based on the AM1/d Hamiltonian is introduced to model chemical glycobiological systems. We included in the parameter training set glycans and the chemical environment often found about them in glycoenzymes. Starting with RM1 and AM1/d-PhoT models we optimized H, C, N, O, and P atomic parameters targeting the best performing molecular properties that contribute to enzyme catalyzed glycan reaction mechanisms. The training set comprising glycans, amino acids, phosphates and small organic model systems was used to derive parameters that reproduce experimental data or high-level density functional results for carbohydrate, phosphate and amino acid heats of formation, amino acid proton affinities, amino acid and monosaccharide dipole moments, amino acid ionization potentials, water-phosphate interaction energies, and carbohydrate ring pucker relaxation times. The result is the AM1/d-Chemical Biology 1 or AM1/d-CB1 model that is considerably more accurate than existing NDDO methods modeling carbohydrates and the amino acids often present in the catalytic domains of glycoenzymes as well as the binding sites of lectins. Moreover, AM1/d-CB1 computed proton affinities, dipole moments, ionization potentials and heats of formation for transition state puckered carbohydrate ring conformations, observed along glycoenzyme catalyzed reaction paths, are close to values computed using DFT M06-2X. AM1/d-CB1 provides a platform from which to accurately model reactions important in chemical glycobiology

Spin-Multiplet Components and Energy Splittings by Multistate Density Functional Theory

Kohn–Sham density functional theory has been tremendously successful in chemistry and physics. Yet, it is unable to describe the energy degeneracy of spin-multiplet components with any approximate functional. This work features two contributions. (1) We present a multistate density functional theory (MSDFT) to represent spin-multiplet components and to determine multiplet energies. MSDFT is a hybrid approach, taking advantage of both wave function theory and density functional theory. Thus, the wave functions, electron densities and energy density-functionals for ground and excited states and for different components are treated on the same footing. The method is illustrated on valence excitations of atoms and molecules. (2) Importantly, a key result is that for cases in which the high-spin components can be determined separately by Kohn–Sham density functional theory, the transition density functional in MSDFT (which describes electronic coupling) can be defined rigorously. The numerical results may be explored to design and optimize transition density functionals for configuration coupling in multiconfigurational DFT

Beyond Kohn–Sham Approximation: Hybrid Multistate Wave Function and Density Functional Theory

A multistate density functional theory (MSDFT) is presented in which the energies and densities for the ground and excited states are treated on the same footing using multiconfigurational approaches. The method can be applied to systems with strong correlation and to correctly describe the dimensionality of the conical intersections between strongly coupled dissociative potential energy surfaces. A dynamic-then-static framework for treating electron correlation is developed to first incorporate dynamic correlation into contracted state functions through block-localized Kohn–Sham density functional theory (KSDFT), followed by diagonalization of the effective Hamiltonian to include static correlation. MSDFT can be regarded as a hybrid of wave function and density functional theory. The method is built on and makes use of the current approximate density functional developed in KSDFT, yet it retains its computational efficiency to treat strongly correlated systems that are problematic for KSDFT but too large for accurate WFT. The results presented in this work show that MSDFT can be applied to photochemical processes involving conical intersections

Connecting Protein Conformational Dynamics with Catalytic Function As Illustrated in Dihydrofolate Reductase

Combined quantum mechanics/molecular mechanics molecular dynamics simulations reveal that the M20 loop conformational dynamics of dihydrofolate reductase (DHFR) is severely restricted at the transition state of the hydride transfer as a result of the M42W/G121V double mutation. Consequently, the double-mutant enzyme has a reduced entropy of activation, i.e., increased entropic barrier, and altered temperature dependence of kinetic isotope effects in comparison with those of wild-type DHFR. Interestingly, in both wild-type DHFR and the double mutant, the average donor–acceptor distances are essentially the same in the Michaelis complex state (∼3.5 Å) and the transition state (2.7 Å). It was found that an additional hydrogen bond is formed to stabilize the M20 loop in the closed conformation in the M42W/G121V double mutant. The computational results reflect a similar aim designed to knock out precisely the dynamic flexibility of the M20 loop in a different double mutant, N23PP/S148A

Chemical Control in the Battle against Fidelity in Promiscuous Natural Product Biosynthesis: The Case of Trichodiene Synthase

Terpene cyclases catalyze the highly stereospecific molding of polyisoprenes into terpenes, which are precursors to most known natural compounds. The isoprenoids are formed via intricate chemical cascades employing rich, yet highly erratic, carbocation chemistry. It is currently not well understood how these biocatalysts achieve chemical control. Here, we illustrate the catalytic control exerted by trichodiene synthase, and in particular, we discover two features that could be general catalytic tools adopted by other terpenoid cyclases. First, to avoid formation of byproducts, the enzyme raises the energy of bisabolyl carbocation, which is a general mechanistic branching point in many sesquiterpene cyclases, resulting in an essentially concerted cyclization cascade. Second, we identify a sulfur–carbocation dative bonding interaction that anchors the bisabolyl cation in a reactive conformation, avoiding tumbling and premature deprotonation. Specifically, Met73 acts as a chameleon, shifting from an initial sulfur−π interaction in the Michaelis complex to a sulfur–carbocation complex during catalysis

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory

We describe a diabatic-at-construction (DAC) strategy for defining diabatic states to determine the adiabatic ground and excited electronic states and their potential energy surfaces using the multistate density functional theory (MSDFT). The DAC approach differs in two fundamental ways from the adiabatic-to-diabatic (ATD) procedures that transform a set of preselected adiabatic electronic states to a new representation. (1) The DAC states are defined in the first computation step to form an active space, whose configuration interaction produces the adiabatic ground and excited states in the second step of MSDFT. Thus, they do not result from a similarity transformation of the adiabatic states as in the ATD procedure; they are the basis for producing the adiabatic states. The appropriateness and completeness of the DAC active space can be validated by comparison with experimental observables of the ground and excited states. (2) The DAC diabatic states are defined using the valence bond characters of the asymptotic dissociation limits of the adiabatic states of interest, and they are strictly maintained at all molecular geometries. Consequently, DAC diabatic states have specific and well-defined physical and chemical meanings that can be used for understanding the nature of the adiabatic states and their energetic components. Here we present results for the four lowest singlet states of LiH and compare them to a well-tested ATD diabatization method, namely the 3-fold way; the comparison reveals both similarities and differences between the ATD diabatic states and the orthogonalized DAC diabatic states. Furthermore, MSDFT can provide a quantitative description of the ground and excited states for LiH with multiple strongly and weakly avoided curve crossings spanning over 10 Å of interatomic separation

Multistate Density Functional Theory for Effective Diabatic Electronic Coupling

Multistate density functional theory (MSDFT) is presented to estimate the effective transfer integral associated with electron and hole transfer reactions. In this approach, the charge-localized diabatic states are defined by block localization of Kohn–Sham orbitals, which constrain the electron density for each diabatic state in orbital space. This differs from the procedure used in constrained density functional theory that partitions the density within specific spatial regions. For a series of model systems, the computed transfer integrals are consistent with experimental data and show the expected exponential attenuation with the donor–acceptor separation. The present method can be used to model charge transfer reactions including processes involving coupled electron and proton transfer

Perturbation Approach for Computing Infrared Spectra of the Local Mode of Probe Molecules

Linear and two-dimensional infrared (IR) spectroscopy of site-specific probe molecules provides an opportunity to gain a molecular-level understanding of the local hydrogen-bonding network, conformational dynamics, and long-range electrostatic interactions in condensed-phase and biological systems. A challenge in computation is to determine the time-dependent vibrational frequencies that incorporate explicitly both nuclear quantum effects of vibrational motions and an electronic structural representation of the potential energy surface. In this paper, a nuclear quantum vibrational perturbation (QVP) method is described for efficiently determining the instantaneous vibrational frequency of a chromophore in molecular dynamics simulations. Computational efficiency is achieved through the use of (a) discrete variable representation of the vibrational wave functions, (b) a perturbation theory to evaluate the vibrational energy shifts due to solvent dynamic fluctuations, and (c) a combined QM/MM potential for the systems. It was found that first-order perturbation is sufficiently accurate, enabling time-dependent vibrational frequencies to be obtained on the fly in molecular dynamics. The QVP method is illustrated in the mode-specific linear and 2D-IR spectra of the H–Cl stretching frequency in the HCl–water clusters and the carbonyl stretching vibration of acetone in aqueous solution. To further reduce computational cost, a hybrid strategy was proposed, and it was found that the computed vibrational spectral peak position and line shape are in agreement with experimental results. In addition, it was found that anharmonicity is significant in the H–Cl stretching mode, and hydrogen-bonding interactions further enhance anharmonic effects. The present QVP method complements other computational approaches, including path integral-based molecular dynamics, and represents a major improvement over the electrostatics-based spectroscopic mapping procedures

Conformational Equilibrium of N‑Myristoylated cAMP-Dependent Protein Kinase A by Molecular Dynamics Simulations

The catalytic subunit of protein kinase A (PKA-C) is subject to several post- or cotranslational modifications that regulate its activity both spatially and temporally. Among those, N-myristoylation increases the kinase affinity for membranes and might also be implicated in substrate recognition and allosteric regulation. Here, we investigated the effects of N-myristoylation on the structure, dynamics, and conformational equilibrium of PKA-C using atomistic molecular dynamics simulations. We found that the myristoyl group inserts into the hydrophobic pocket and leads to a tighter packing of the A-helix against the core of the enzyme. As a result, the conformational dynamics of the A-helix are reduced and its motions are more coupled with the active site. Our simulations suggest that cation−π interactions among W30, R190, and R93 are responsible for coupling these motions. Two major conformations of the myristoylated N-terminus are the most populated: a long loop (LL conformation), similar to Protein Data Bank (PDB) entry 1CMK, and a helix–turn–helix structure (HTH conformation), similar to PDB entry 4DFX, which shows stronger coupling between the conformational dynamics observed at the A-helix and active site. The HTH conformation is stabilized by S10 phosphorylation of the kinase via ionic interactions between the protonated amine of K7 and the phosphate group on S10, further enhancing the dynamic coupling to the active site. These results support a role of N-myristoylation in the allosteric regulation of PKA-C