Density functional self-consistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties: Applications to solvated water and formaldehyde

A combined quantum mechanics/molecular mechanics (QM/MM) method is described, where the polarization between the solvent and solute is accounted for using a self-consistent scheme linear in the solvent polarization. The QM/MM method is implemented for calculation of energies and molecular response properties including the calculation of linear and quadratic response functions using the density-functional theory (DFT) and the Hartree-Fock (HF) theory. Sample calculations presented for ground-state energies, first-order ground-state properties, excitation energies, first-order excited state properties, polarizabilities, first-hyperpolarizabilities, and two-photon absorptions strengths of formaldehyde suggests that DFT may in some cases be a sufficiently reliable alternative to high-level theory, such as coupled-cluster (CC) theory, in modeling solvent shifts, whereas results obtained with the HF wave function deviate significantly from the CC results. Calculations carried out on water gives results that also are comparable with CC calculations in accuracy for ground-state and first-order properties. However, to obtain such accuracy an exchange-correlation functional capable of describing the diffuse Rydberg states must be chosen.     

Two-photon absorption cross sections: an investigation of solvent effects. Theoretical studies on formaldehyde and water

The effects of a solvent on the two-photon absorption of microsolvated formaldehyde and liquid water have been studied using hybrid coupled-cluster/molecular mechanics (CC/MM) response theory. Both water and formaldehyde were considered solvated in water, where the solvent water molecules were described within the framework of molecular mechanics. Prior to the CC/MM calculations, molecular dynamics simulations were performed on the water/formaldehyde and water/water aggregates and many configurations were generated. By carrying out CC/MM response calculations on the individual configurations, it was possible to obtain statistically averaged results for both the excitation energies and two-photon absorption cross sections. For liquid water, the comparison between one- and two-photon absorption spectra is in good agreement with the experimental data available in the literature. In particular, the lowest energy transition occurring in the one-photon absorption spectrum of water only occurs with a relatively small strength in the two-photon absorption spectrum. This result is important for the interpretation of two-photon absorption data as these results show that in the absence of selection rules that determine which transitions are forbidden, the spectral profile of the two-photon absorption spectrum can be significantly different from the spectral profile of the one-photon absorption spectrum.     

Statistical mechanically averaged molecular properties of liquid water calculated using the combined coupled cluster/molecular dynamics method

Liquid water is investigated theoretically using combined molecular dynamics (MD) simulations and accurate electronic structure methods. The statistical mechanically averaged molecular properties of liquid water are calculated using the combined coupled cluster/molecular mechanics (CC/MM) method for a large number of configurations generated from MD simulations. The method includes electron correlation effects at the coupled cluster singles and doubles level and the use of a large correlation consistent basis set. A polarizable force field has been used for the molecular dynamics part in both the CC/MM method and in the MD simulation. We describe how the methodology can be optimized with respect to computational costs while maintaining the quality of the results. Using the optimized method we study the energetic properties including the heat of vaporization and electronic excitation energies as well as electric dipole and quadrupole moments, the frequency dependent electric (dipole) polarizability, and electric-field-induced second harmonic generation first and second hyperpolarizabilities. Comparisons with experiments are performed where reliable data are available. Furthermore, we discuss the important issue on how to compare the calculated microscopic nonlocal properties to the experimental macroscopic measurements.     

Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins

The explicit treatment of polarization as a many-body interaction in condensed-phase systems represents a current problem in empirical force-field development. Although a variety of efficient models for molecular polarization have been suggested, polarizable force fields are still far from common use nowadays. In this work, we consider interactive polarization models employing Thole's short-range damping scheme and assess them for application on polypeptides. Despite the simplicity of the model, we find mean polarizabilities and anisotropies of amino acid side chains in excellent agreement with MP2/cc-pVQZ benchmark calculations. Combined with restrained electrostatic potential (RESP) derived atomic charges, the models are applied in a quantum-mechanical/molecular-mechanical (QM/MM) approach. An iterative scheme is used to establish a self-consistent mutual polarization between the QM and MM moieties. This ansatz is employed to study the influence of the protein polarizability on calculated optical properties of the protonated Schiff base of retinal in rhodopsin (Rh), bacterio-rhodopsin (bR), and pharaonis sensory rhodopsin II (psRII). The shifts of the excitation energy due to the instantaneous polarization response of the protein to the charge transfer on the retinal chromophore are quantified using the high level ab initio multireference spectroscopy-oriented configuration interaction (SORCI) method. The results are compared with those of previously published QM1/QM2/MM models for bR and psRII.     

Uptake of phenol on aerosol particles

We present a study of the interaction between a phenol molecule and an aerosol particle. The aerosol particle is represented by a cluster of 128 water molecules. Using a classical approach, we present interaction energy surfaces for different relative distances and for three orientations of phenol relative to the particle. From the energy surfaces we find the reaction pathways with the largest interaction between the molecule and the particle. We use a quantum mechanics/molecular mechanics (QM/MM) method to calculate a potential energy curve for each reaction path. Coupled cluster methods are used for the part of the system described by quantum mechanics, while the part described by molecular mechanics is represented by a polarizable force field. We compare results obtained from the classical approach with the QM/MM results. Furthermore, we use the QM/MM results to calculate mass accommodation coefficients using a quantum-statistical (QM-ST) model and show how the mass accommodation coefficient depends on the relative orientation of phenol with respect to the aerosol particle.     

New QM/MM implementation of the DFTB3 method in the gromacs package

The approximate density‐functional tight‐binding theory method DFTB3 has been implemented in the quantum mechanics/molecular mechanics (QM/MM) framework of the Gromacs molecular simulation package. We show that the efficient smooth particle–mesh Ewald implementation of Gromacs extends to the calculation of QM/MM electrostatic interactions. Further, we make use of the various free‐energy functionalities provided by Gromacs and the PLUMED plugin. We exploit the versatility and performance of the current framework in three typical applications of QM/MM methods to solve biophysical problems: (i) ultrafast proton transfer in malonaldehyde, (ii) conformation of the alanine dipeptide, and (iii) electron‐induced repair of a DNA lesion. Also discussed is the further development of the framework, regarding mostly the options for parallelization. © 2015 Wiley Periodicals, Inc.     

The QM‐MM interface for CHARMM‐deMon

We present a new QM/MM interface for fast and efficient simulations of organic and biological molecules. The CHARMM/deMon interface has been developed and tested to perform minimization and atomistic simulations for multi‐particle systems. The current features of this QM/MM interface include readability for molecular dynamics, tested compatibility with Free Energy Perturbation simulations (FEP) using the dual topology/single coordinate method. The current coupling scheme uses link atoms, but further extensions of the code to incorporate other available schemes are planned. We report the performance of different levels of theory for the treatment of the QM region, while the MM region was represented by a classical force‐field (CHARMM27) or a polarizable force‐field based on a simple Drude model. The current QM/MM implementation can be coupled to the dual‐thermostat method and the VV2 integrator to run molecular dynamics simulations. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A combined quantum mechanical and molecular mechanical method using modified generalized hybrid orbitals: implementation for electronic excited states

The generalized hybrid orbital (GHO) method is implemented at the second-order approximate coupled cluster singles and doubles (CC2) level for quantum mechanical (QM)/molecular mechanical (MM) electronic excited state calculations. The linear response function of CC2 in the GHO scheme is derived and implemented. The new implementation is applied to the first singlet excited states of three aromatic amino acids, phenylalanine, tyrosine, and tryptophan, and also bacteriorhodopsin for assessment. The results obtained for aromatic amino acids agreed well with the full QM CC2 calculations, while the calculated excitation energies of bacteriorhodopsin and its chromophore, all-trans retinal, reproduced the environmental shift of the experimental data. For the bacteriorhodopsin case, the environmental shift of GHO also showed good agreements with the experimental data. The contribution of the quantum effect of certain moieties in the excited states is elucidated by changing the partitioning of QM and MM regions.     

Conformational simulations of aqueous solvated alpha-conotoxin GI and its single disulfide analogues using a polarizable force field model

The solution conformation of alpha-conotoxin GI and its two single disulfide analogues are simulated using a polarizable force field in combination with the molecular fragmentation quantum chemical calculation. The polarizability is explicitly described by allowing the partial charges and fragment dipole moments to be variables, with values coming from the linear-scaling energy-based molecular fragmentation calculations at the B3LYP/6-31G(d) level. In comparison with the full quantum chemical calculations, the fragmentation approaches can yield precise ground-state energies, dipole moments, and static polarizabilities for peptides. The B3LYP/6-31G(d) charges and fragment-centered dipole moments are introduced in calculations of electrostatic terms in both AmberFF03 and OPLS force fields. Our test calculations on the gas-phase glucagon (PDB code: 1gcn) and solvated alpha-conotoxin GI (PDB code: 1not) demonstrate that the present polarization model is capable of describing the structural properties (such as the relative conformational energies, intramolecular hydrogen bonds, and disulfide bonds) with accuracy comparable to some other polarizable force fields (ABEEM/MM and OPLS-PFF) and the quantum mechanics/molecular mechanics (QM/MM) hybrid model. The employment of fragment-centered dipole moments in calculations of dipole-dipole interactions can save computational time in comparison with those polarization models using atom-centered dipole moments without much loss of accuracy. The molecular dynamics simulations using the polarizable force field demonstrate that two single disulfide GI analogues are more flexible and less structured than the native alpha-conotoxin GI, in agreement with NMR experiments. The polarization effect is important in simulations of the folding/unfolding process of solvated proteins.     

Implementation of the IMOMM methodology for performing combined QM/MM molecular dynamics simulations and frequency calculations

A technique for implementing the integrated molecular orbital and molecular mechanics (IMOMM) methodology developed by Maseras and Morokuma that is used to perform combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, frequency calculations and simulations of macromolecules including explicit solvent is presented. Although the IMOMM methodology is generalized to any coordinate system, the implementation first described by Maseras and Morokuma requires that the QM and MM gradients be transformed into internal coordinates before they are added together. This coordinate transformation can be cumbersome for macromolecular systems and can become ill-defined during the course of a molecular dynamics simulation. We describe an implementation of the IMOMM method in which the QM and MM gradients are combined in the cartesian coordinate system, thereby avoiding potential problems associated with using the internal coordinate system. The implementation can be used to perform combined QM/MM molecular dynamics simulations and frequency calculations within the IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM frequency calculations. Received: 11 May 1998 / Accepted: 14 August 1998 / Published online: 16 November 1998     

The coupling constant polarizability and hyperpolarizabilty of 1J(NH) in N-methylacetamide, and its application for the multipole spin-spin coupling constant polarizability/reaction field approach to solvation

We present a benchmark study of a combined multipole spin-spin coupling constant (SSCC) polarizability/reaction field (MJP/RF) approach to the calculation of both specific and bulk solvation effects on SSCCs of solvated molecules. The MJP/RF scheme is defined by an expansion of the SSCCs of the solvated molecule in terms of coupling constant dipole and quadrupole polarizabilities and hyperpolarizabilities derived from single molecule ab initio calculations. The solvent electric field and electric field gradient are calculated based on data derived from molecular dynamics (MD) simulations thereby accounting for solute-solvent dynamical effects. The MJP/RF method is benchmarked against polarizable QM/MM calculations for the one-bond N-H coupling constant in N-methylacetamide. The best agreement between the MJP/RF and QM/MM approaches is found by truncating the electric field expansion in the MJP/RF approach at the linear electric field level. In addition, we investigate the sensitivity of the results due to the choice of one-electron basis set in the ab initio calculations of the coupling constant (hyper-)polarizabilities and find that they are affected by the basis set in a way similar to the coupling constants themselves.     

Calculating absorption shifts for retinal proteins: computational challenges

Rhodopsins can modulate the optical properties of their chromophores over a wide range of wavelengths. The mechanism for this spectral tuning is based on the response of the retinal chromophore to external stress and the interaction with the charged, polar, and polarizable amino acids of the protein environment and is connected to its large change in dipole moment upon excitation, its large electronic polarizability, and its structural flexibility. In this work, we investigate the accuracy of computational approaches for modeling changes in absorption energies with respect to changes in geometry and applied external electric fields. We illustrate the high sensitivity of absorption energies on the ground-state structure of retinal, which varies significantly with the computational method used for geometry optimization. The response to external fields, in particular to point charges which model the protein environment in combined quantum mechanical/molecular mechanical (QM/MM) applications, is a crucial feature, which is not properly represented by previously used methods, such as time-dependent density functional theory (TDDFT), complete active space self-consistent field (CASSCF), and Hartree-Fock (HF) or semiempirical configuration interaction singles (CIS). This is discussed in detail for bacteriorhodopsin (bR), a protein which blue-shifts retinal gas-phase excitation energy by about 0.5 eV. As a result of this study, we propose a procedure which combines structure optimization or molecular dynamics simulation using DFT methods with a semiempirical or ab initio multireference configuration interaction treatment of the excitation energies. Using a conventional QM/MM point charge representation of the protein environment, we obtain an absorption energy for bR of 2.34 eV. This result is already close to the experimental value of 2.18 eV, even without considering the effects of protein polarization, differential dispersion, and conformational sampling.     

A discrete interaction model/quantum mechanical method to describe the interaction of metal nanoparticles and molecular absorption

A frequency-dependent quantum mechanics/molecular mechanics method for the calculation of response properties of molecules adsorbed on metal nanoparticles is presented. This discrete interaction model/quantum mechanics (DIM/QM) method represents the nanoparticle atomistically, thus accounting for the local environment of the nanoparticle surface on the optical properties of the adsorbed molecule. Using the DIM/QM method, we investigate the coupling between the absorption of a silver nanoparticle and of a substituted naphthoquinone. This system is chosen since it shows strong coupling due to a molecular absorption peak that overlaps with the plasmon excitation in the metal nanoparticle. We show that there is a strong dependence not only on the distance of the molecule from the metal nanoparticle but also on its orientation relative to the nanoparticle. We find that when the transition dipole moment of an excitation is oriented towards the nanoparticle there is a significant increase in the molecular absorption as a result of coupling to the metal nanoparticle. In contrast, we find that the molecular absorption is decreased when the transition dipole moment is oriented parallel to the metal nanoparticle. The coupling between the molecule and the metal nanoparticle is found to be surprisingly long range and important on a length scale comparable to the size of the metal nanoparticle. A simple analytical model that describes the molecule and the metal nanoparticle as two interacting point objects is found to be in excellent agreement with the full DIM/QM calculations over the entire range studied. The results presented here are important for understanding plasmon-exciton hybridization, plasmon enhanced photochemistry, and single-molecule surface-enhanced Raman scattering.