Full QM Calculations Research Articles

A Polarizable QM/MM Model That Combines the State-Averaged CASSCF and AMOEBA Force Field for Photoreactions in Proteins.

This study presents the polarizable quantum mechanics/molecular mechanics (QM/MM) embedding of the state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field for the purpose of studying photoreactions in protein environments. We describe two extensions of our previous work that combine SA-CASSCF with AMOEBA water models, allowing it to be generalized to AMOEBA models for proteins and other macromolecules. First, we discuss how our QM/MM model accounts for the discrepancy between the direct and polarization electric fields that arises in the AMOEBA description of intramolecular polarization. A second improvement is the incorporation of link atom schemes to treat instances in which the QM/MM boundary goes through covalent bonds. A single-link atom scheme and double-link atom scheme are considered in this work, and we will discuss how electrostatic interaction, van der Waals interaction, and various kinds of valence terms are treated across the boundary. To test the accuracy of the link atom scheme, we will compare QM/MM with full QM calculations and study how the errors in ground state properties, excited state properties, and excitation energies change when tuning the parameters in the link atom scheme. We will also test the new SA-CASSCF/AMOEBA method on an elementary reaction step in NanoLuc, an artificial bioluminescence luciferase. We will show how the reaction mechanism is different when calculated in the gas phase, in polarizable continuum medium (PCM), versus in protein AMOEBA models.

Toward a numerically efficient description of bulk-solvated anionic states.

We investigate the vertical electron attachment energy (VAE) of 1-methyl-4-nitroimidazole, a model radiosensitizer, employing quantum mechanics/molecular mechanics (QM/MM) and QM/polarized continuum (QM/PCM) solvation models. We considered the solvent-excluded surface (QM/PCM-SES) and Van der Waals (QM/PCM-VDW) cavities within the PCM framework, the electrostatic embedding QM/MM (EE-QM/MM) model, and the self-consistent sequential QM/MM polarizable electrostatic embedding (scPEE-S-QM/MM) model. Due to slow VAE convergence concerning the number of QM solvent molecules, full QM calculations prove inefficient. Ensemble averages in these calculations do not align with VAEs computed for the representative solute-solvent configuration. QM/MM and QM/PCM calculations show agreement with each other for sufficiently large QM regions, although the QM/PCM-VDW model exhibits artifacts linked to the cavity. QM/MM models demonstrate good agreement between ensemble averages and VAEs calculated with the representative configuration. Notably, the VAE computed with the scPEE-S-QM/MM model achieves faster convergence concerning the number of QM water molecules compared to the EE-QM/MM model, attributed to enhanced efficiency from MM charge polarization in the scPEE-S-QM/MM approach. This emphasizes the importance of QM/classical models with accurate solute-solvent and solvent-solvent mutual polarization for obtaining converged VAEs at a reasonable computational cost. The full-QM approach is very inefficient, while the microsolvation model is inaccurate. Computational savings in QM/MM models result from electrostatic embedding and the representative configuration, with the scPEE-S-QM/MM approach emerging as an efficient tool for describing bulk-solvated anions within the QM/MM framework. Its potential extends to improving transient anion state descriptions in biomolecules and radiosensitizers, especially given the frequent employment of microsolvation models.

Analytic high-order energy derivatives for metal nanoparticle-mediated infrared and Raman scattering spectra within the framework of quantum mechanics/molecular mechanics model with induced charges and dipoles.

This work is devoted to deriving and implementing analytic second- and third-order energy derivatives with respect to the nuclear coordinates and external electric field within the framework of the hybrid quantum mechanics/molecular mechanics method with induced charges and dipoles (QM/DIM). Using these analytic energy derivatives, one can efficiently compute the harmonic vibrational frequencies, infrared (IR) and Raman scattering (RS) spectra of the molecule in the proximity of noble metal clusters/nanoparticles. The validity and accuracy of these analytic implementations are demonstrated by the comparison of results obtained by the finite-difference method and the analytic approaches and by the full QM and QM/DIM calculations. The complexes formed by pyridine and two sizes of gold clusters (Au18 and Au32) at varying intersystem distances of 3, 4, and 5 Å are used as the test systems, and Raman spectra of 4,4'-bipyridine in the proximity of Au2057 and Ag2057 metal nanoparticles (MNP) are calculated by the QM/DIM method and compared with experimental results as well. We find that the QM/DIM model can well reproduce the IR spectra obtained from full QM calculations for all the configurations, while although it properly enhances some of the vibrational modes, it artificially overestimates RS spectral intensities of several modes for the systems with very short intersystem distance. We show that this could be improved, however, by incorporating the hyperpolarizability of the gold metal cluster in the evaluation of RS intensities. Additionally, we address the potential impact of charge migration between the adsorbate and MNPs.

Machine learning builds full-QM precision protein force fields in seconds.

Full-quantum mechanics (QM) calculations are extraordinarily precise but difficult to apply to large systems, such as biomolecules. Motivated by the massive demand for efficient calculations for large systems at the full-QM level and by the significant advances in machine learning, we have designed a neural network-based two-body molecular fractionation with conjugate caps (NN-TMFCC) approach to accelerate the energy and atomic force calculations of proteins. The results show very high precision for the proposed NN potential energy surface models of residue-based fragments, with energy root-mean-squared errors (RMSEs) less than 1.0kcal/mol and force RMSEs less than 1.3kcal/mol/Å for both training and testing sets. The proposed NN-TMFCC method calculates the energies and atomic forces of 15 representative proteins with full-QM precision in 10-100s, which is thousands of times faster than the full-QM calculations. The computational complexity of the NN-TMFCC method is independent of the protein size and only depends on the number of residue species, which makes this method particularly suitable for rapid prediction of large systems with tens of thousands or even hundreds of thousands of times acceleration. This highly precise and efficient NN-TMFCC approach exhibits considerable potential for performing energy and force calculations, structure predictions and molecular dynamics simulations of proteins with full-QM precision.

Avoiding Electron Spill-Out in QM/MM Calculations on Excited States with Simple Pseudopotentials.

QM/MM calculations of electronic excitations with diffuse basis sets often have large errors due to spill-out of electrons from the quantum subsystem. The Pauli repulsion of the electrons by the environment has to be included to avoid this. We propose transferable atomic all-electron pseudopotentials that can readily be combined with most MM force fields to avoid electron spill-out. QM/MM excitation energies computed with time-dependent Hartree-Fock and the algebraic diagrammatic construction through second-order are benchmarked against supermolecular calculations to validate these new pseudopotentials. The QM/MM calculations with pseudopotentials give accurate results that are stable with augmentation of the basis set with diffuse functions. We show that the largest contribution to residual deviations from full QM calculations is caused by the missing London dispersion interaction.

The effect of polarizable environment on two-photon absorption cross sections characterized by the equation-of-motion coupled-cluster singles and doubles method combined with the effective fragment potential approach.

We report an extension of a hybrid polarizable embedding method incorporating solvent effects in the calculations of two-photon absorption (2PA) cross sections. We employ the equation-of-motion coupled-cluster singles and doubles method for excitation energies (EOM-EE-CCSD) for the quantum region and the effective fragment potential (EFP) method for the classical region. We also introduce a rigorous metric based on 2PA transition densities for assessing the domain of applicability of QM/MM (quantum mechanics/molecular mechanics) schemes for calculating 2PA cross sections. We investigate the impact of the environment on the 2PA cross sections of low-lying transitions in microhydrated clusters of para-nitroaniline, thymine, and the deprotonated anionic chromophore of photoactive yellow protein (PYPb). We assess the performance of EOM-EE-CCSD/EFP by comparing the 2PA cross sections against full QM calculations as well as against the non-polarizable QM/MM electrostatic embedding approach. We demonstrate that the performance of QM/EFP improves when few explicit solvent molecules are included in the QM subsystem. We correlate the errors in the 2PA cross sections with the errors in the key electronic properties-identified by the analysis of 2PA natural transition orbitals and 2PA transition densities-such as excitation energies, transition moments, and dipole-moment differences between the initial and final states. Finally, using aqueous PYPb, we investigate the convergence of 2PA cross sections to bulk values.

Performance of the AMOEBA Water Model in the Vicinity of QM Solutes: A Diagnosis Using Energy Decomposition Analysis.

The importance of incorporating solvent polarization effects into the modeling of solvation processes has been well-recognized, and therefore a new generation of hybrid quantum mechanics/molecular mechanics (QM/MM) approaches that accounts for this effect is desirable. We present a fully self-consistent, mutually polarizable QM/MM scheme using the AMOEBA force field, in which the total energy of the system is variationally minimized with respect to both the QM electronic density and the MM induced dipoles. This QM/AMOEBA model is implemented through the Q-Chem/LibEFP code interface and then applied to the evaluation of solute-solvent interaction energies for various systems ranging from the water dimer to neutral and ionic solutes (NH3, NH4+, CN-) surrounded by increasing numbers of water molecules (up to 100). In order to analyze the resulting interaction energies, we also utilize an energy decomposition analysis (EDA) scheme which identifies contributions from permanent electrostatics, polarization, and van der Waals (vdW) interaction for the interaction between the QM solute and the solvent molecules described by AMOEBA. This facilitates a component-wise comparison against full QM calculations where the corresponding energy components are obtained via a modified version of the absolutely localized molecular orbitals (ALMO)-EDA. The results show that the present QM/AMOEBA model can yield reasonable solute-solvent interaction energies for neutral and cationic species, while further scrutiny reveals that this accuracy highly relies on the delicate balance between insufficiently favorable permanent electrostatics and softened vdW interaction. For anionic solutes where the charge penetration effect becomes more pronounced, the QM/MM interface turns out to be unbalanced. These results are consistent with and further elucidate our findings in a previous study using a slightly different QM/AMOEBA model ( Dziedzic et al. J. Chem. Phys. 2016 , 145 , 124106 ). The implications of these results for further refinement of this model are also discussed.

Electronic spectroscopy of a solvatochromic dye in water: comparison of static cluster/implicit and dynamical/explicit solvent models on structures and energies

In this study, we analyze the photophysics of the N-methyl-6-oxyquinolinium betaine (MQ) solvatochromic dye in aqueous solution, focussing on the important structural rearrangement of its first solvation shell following the electronic excitation, which is characterized by a strong charge transfer. To this aim, we compare the results provided by ground- and excited-state ab-initio molecular dynamics with that of full QM calculations on clusters including a small number of solvent molecules (from 1 to 4), taking into account bulk solvent effects by the Polarizable Continuum Model. The two methods agree in predicting that while in the ground electronic state between three and four water molecules are strongly coordinated to the oxygen atom of MQ, in the excited state two water molecules are present in the first solvation layer of the MQ oxygen. Vertical excitation and emission energies computed on the structures provided by the two approaches allow for estimates of the Stokes shift consistent with the experimental results. On the ground of the present results, some general considerations on the advantages and limitations of the dynamical and static approaches in describing a photoactivated process in solution are proposed.

Extension of the Effective Fragment Potential Method to Macromolecules.

The effective fragment potential (EFP) approach, which can be described as a nonempirical polarizable force field, affords an accurate first-principles treatment of noncovalent interactions in extended systems. EFP can also describe the effect of the environment on the electronic properties (e.g., electronic excitation energies and ionization and electron-attachment energies) of a subsystem via the QM/EFP (quantum mechanics/EFP) polarizable embedding scheme. The original formulation of the method assumes that the system can be separated, without breaking covalent bonds, into closed-shell fragments, such as solvent and solute molecules. Here, we present an extension of the EFP method to macromolecules (mEFP). Several schemes for breaking a large molecule into small fragments described by EFP are presented and benchmarked. We focus on the electronic properties of molecules embedded into a protein environment and consider ionization, electron-attachment, and excitation energies (single-point calculations only). The model systems include chromophores of green and red fluorescent proteins surrounded by several nearby amino acid residues and phenolate bound to the T4 lysozyme. All mEFP schemes show robust performance and accurately reproduce the reference full QM calculations. For further applications of mEFP, we recommend either the scheme in which the peptide is cut along the Cα-C bond, giving rise to one fragment per amino acid, or the scheme with two cuts per amino acid, along the Cα-C and Cα-N bonds. While using these fragmentation schemes, the errors in solvatochromic shifts in electronic energy differences (excitation, ionization, electron detachment, or electron-attachment) do not exceed 0.1 eV. The largest error of QM/mEFP against QM/EFP (no fragmentation of the EFP part) is 0.06 eV (in most cases, the errors are 0.01-0.02 eV). The errors in the QM/molecular mechanics calculations with standard point charges can be as large as 0.3 eV.

Contributions of pauli repulsions to the energetics and physical properties computed in QM/MM methods

Conventional combined quantum mechanical/molecular mechanical (QM/MM) methods lack explicit treatment of Pauli repulsions between the quantum-mechanical and molecular-mechanical subsystems. Instead, classical Lennard-Jones (LJ) potentials between QM and MM nuclei are used to model electronic Pauli repulsion and long-range London dispersion, despite the fact that the latter two are inherently of quantum nature. Use of the simple LJ potential in QM/MM methods can reproduce minimal geometries and energies of many molecular clusters reasonably well, as compared to full QM calculations. However, we show here that the LJ potential cannot correctly describe subtle details of the electron density of the QM subsystem because of the neglect of Pauli repulsions between the QM and MM subsystems. The inaccurate electron density subsequently affects the calculation of electronic and magnetic properties of the QM subsystem. To explicitly consider Pauli interactions with QM/MM methods, we propose a method to use empirical effective potentials on the MM atoms. The test case of the binding energy and magnetic properties of a water dimer shows promising results for the general application of effective potentials to mimic Pauli repulsions in QM/MM calculations.

Selection and Validation of Charge and Lennard-Jones Parameters for QM/MM Simulations of Hydrocarbon Interactions with Zeolites.

Quantum mechanics/molecular mechanics (QM/MM) models are an appealing method for performing zeolite simulations. In QM/MM, a small cluster chosen to encompass the active center is described by QM, while the rest of the zeolite is described by MM. In the present study, we demonstrate that the charges and Lennard-Jones parameters on Si and O must be chosen properly for QM/MM calculations of adsorption energies and activation energies to agree closely with full QM calculations. The selection of parameters for Si and O is based on using the ωB97X-D functional for DFT calculations of the QM region, which is effective in capturing the effects of van der Waals interactions. A comparison of the heats of adsorption for a variety of adsorbates and activation energies for the cracking of propane and butane reveals that energies derived from QM/MM calculation carried out with appropriately selected MM parameters agree to within an rms error of ∼1.5 kcal/mol with QM calculations. To avoid reparametrization for new substrates, Lennard-Jones zeolite parameters are chosen to be compatible with existing CHARMM parameters. Transferability of these parameters is demonstrated by tests utilizing the B3LYP density functional and simulations of MFI and FAU zeolites. Moreover, the computational time for QM/MM calculations is considerably lower than that for QM calculations, and the ratio of computational times decreases rapidly with increasing size of the cluster used to represent the zeolite.

Flexible-boundary QM/MM calculations: II. Partial charge transfer across the QM/MM boundary that passes through a covalent bond

Recently, based on the principle of electronic chemical potential equalization and the principle of charge conservation, we proposed a flexible-boundary scheme that allows both partial charge transfer and self-consistent polarization between the quantum mechanical (QM) and molecular mechanical (MM) subsystems in QM/MM calculations; the scheme was applied to study the atomic charges in selected ion–solvent complexes. In the present contribution, we further extend the flexible-boundary treatment to handle the QM/MM boundary passing through covalent bonds. We find that the flexible-boundary redistributed charge and dipole schemes yield reasonable agreement with full-QM calculations for a number of molecular ions and amino acids with charged side chains. Using the full-QM results as reference, the mean unsigned deviations are computed to be 0.06 e for atomic partial charges of the QM atoms, 0.11 e for the amounts of charge transfer between the QM and MM subsystems, and 0.016 A for the lengths of the covalent bonds that directly connect the QM and MM subsystems. The results indicate the importance of accounting for partial charge transfer across the QM/MM boundary when the QM subsystems are charged.

Quantitative Assessment of Electrostatic Embedding in Density Functional Theory Calculations of Biomolecular Systems.

We evaluate the accuracy of density functional theory quantum calculations of biomolecular subsystems using a simple electrostatic embedding scheme. Our scheme is based on dividing the system of interest into a primary and secondary subsystem. A finite difference discretization of the Kohn-Sham equations is used for the primary subsystem, while its electrostatic environment is modeled with a simple one-electron potential. Force-field atomic partial charges are used to generate smeared Gaussian charge densities and to model the secondary subsystem. We illustrate the utility of this approach with calculations of truncated dipeptide chains. We analyze quantitatively the accuracy of this approach by calculating atomic forces and comparing results with full QM calculations. The impact of the choice made in terminating dangling bonds at the frontier of the QM region is also investigated.

An ONIOM Study of a Guanidinium Salt Ionic Liquid. Experimental and Computational Characterization of N,N,N`,N`,N``-Pentabutyl-N``-benzylguanidinium Bromide

The guanidinium salt-based ionic liquid N,N,N`,N`,N``-pentabutyl-N``-benzyl-guanidinium bromide was synthesized and characterized by 1H and 13C NMR spectroscopy in solution and by single crystal X-ray structure analysis. The MO computational hybrid method of Morokuma and coworkers (ONIOM method) is applied to compare experimental and quantum chemical results. Four calculation models for two layer ONIOM calculations are defined based on differences of the area for the high-level layer region. Optimized geometries, interaction energies between the cation and the anion, and atomic charges are compared to data of full-QM calculations for the optimized geometry as well as of an experimental X-ray structure determination. The results indicate that it is mandatory for obtaining reasonable results that the parts of the substituent groups which are directly bound to the amino nitrogen atoms are included into the high-level layer. This least required ONIOM model for guanidinium-type ionic liquids can save computational cost of 90% compared to the full-QM SCF calculation.

Analysis of polarization in QM/MM modelling of biologically relevant hydrogen bonds

Combined quantum mechanics/molecular mechanics (QM/MM) methods are increasingly important for the study of chemical reactions and systems in condensed phases. Here, we have tested the accuracy of a density functional theory-based QM/MM implementation (B3LYP/6-311+G(d,p)/CHARMM27) on a set of biologically relevant interactions by comparison with full QM calculations. Intermolecular charge transfer due to hydrogen bond formation is studied to assess the severity of spurious polarization of QM atoms by MM point charges close to the QM/MM boundary. The changes in total electron density and natural bond orbital atomic charges due to hydrogen bond formation in selected complexes obtained at the QM/MM level are compared with full QM results. It is found that charge leakage from the QM atoms to MM atomic point charges close to the QM/MM boundary is not a serious problem, at least with limited basis sets. The results are encouraging in showing that important properties of key biomolecular interactions can be treated well at the QM/MM level employing good-quality levels of QM theory.

Flexible-Boundary Quantum-Mechanical/Molecular-Mechanical Calculations: Partial Charge Transfer between the Quantum-Mechanical and Molecular-Mechanical Subsystems.

Based on the principle of electronic chemical potential equalization, we propose a flexible-boundary scheme to account for partial charge transfers between the quantum-mechanical (QM) and molecular-mechanical (MM) subsystems in combined QM/MM calculations. The QM subsystem is viewed as an open system with a fluctuating number of electrons and is described by a statistical mixture of ensemble that consists of states of integer number of electrons. The MM subsystem serves as a reservoir that exchanges electrons with the QM subsystem. The electronic chemical potential of the MM subsystem varies whenever charges flow in or out, until equilibrium is established for the electronic chemical potentials between the QM and MM subsystems. Our scheme is demonstrated by calculations of the partial atomic charges for 7 small model systems, each consisting of a singly charged ion and a water molecule, as well as for the Eigen cation, a model system for the solvated structure of hydronium ion in water. Encouraging results are obtained for the partial atomic charges, which are in reasonable agreement with full-QM calculations on those model systems. The averaged mean unsigned deviations between the QM/MM and full-QM calculations are 0.16 e for the partial atomic charges of the entire systems and 0.13 e for the amount of charge transferred between the QM and MM subsystems.

One-electron quantum capping potential for hybrid QM/MM studies of silicate molecules and solids

A one-electron quantum capping potential (QCP) for replacing the oxygen atom in silicate-type systems is developed. It is used to border the quantum region in a hybrid quantum mechanics/molecular mechanics (QM/MM) study. Its parametrization has been verified comparing the structures and atomic populations of silicate molecules with those provided by full QM calculations. The method has also been tested for the structure and 29Si NMR shieldings of a mazzite cluster bordered with oxygen QCPs.

Removing extra frontier parameters in QM/MM methods : a tentative with the Local Self-Consistent Field approach

We present a new quantum mechanics/molecular mechanics (QM/MM) scheme based on the Local-SCF method that avoids the extra-parametrization of the QM/MM frontier by taking into account the core electrons of the hybrid frontier atoms by means of self-consistent core orbitals (SCCO). This study follows and extends our previous investigation based on frozen core orbitals (FCO) [Chem. Phys. Lett. 427 236-240(2006)]. Test calculations on small organic compounds show that the most common atoms found in biochemical systems can be used as frontier atoms without adding any parameters, and that only relatively small geometric and energetic deviations compared to full-QM calculations are generated.

Self-Consistent Polarization of the Boundary in the Redistributed Charge and Dipole Scheme for Combined Quantum-Mechanical and Molecular-Mechanical Calculations.

The recently developed redistributed charge (RC) and redistributed charge and dipole (RCD) schemes are electrostatic-embedding schemes to treat a quantum-mechanical/molecular- mechanical (QM/MM) boundary that passes through covalent bonds. In the RC and RCD schemes, the QM subsystem is polarized by the MM subsystem, but the MM subsystem is not polarized by the QM one; this results in an unbalanced treatment of the electrostatic interactions. In the work reported here, we developed improved schemes, namely, the polarized-boundary RC scheme (PBRC) and the polarized-boundary RCD (PBRCD) scheme, by adding self-consistent mutual polarization of the boundary region of the MM subsystem to the previous schemes. The mutual polarizations are accounted for in the polarized-boundary calculations by adjusting the boundary-region MM point charges according to the principles of electronegativity equalization and charge conservation until the charge distributions in both the QM subsystem and the polarizable region of the MM subsystem converge. In particular, we implemented three literature parametrizations of electronegativity equalization: the original electronegativity equalization method (EEM) by Mortier and co-workers, the charge equalization (QEq) method proposed by Rappé and Goddard, and a modified version of the QEq method by Bakowies and Thiel. The PBRC and PBRCD schemes were tested by calculating proton affinities for small organic compounds and capped amino acids. As compared to full-QM calculations, the PBRC and PBRCD schemes produced more accurate proton affinities, on average, than the original RC and RCD methods; the mean unsigned error in proton affinities is reduced from about 5 kcal/mol to 3 kcal/mol with little change in geometry. The improvement is encouraging and illustrates the importance of mutual polarization of the QM and MM subsystems in treating reactions where noticeable charge transfer occurs in the QM subsystem.

QM/MM Modeling of Enantioselective Pybox–Ruthenium‐ and Box–Copper‐Catalyzed Cyclopropanation Reactions: Scope, Performance, and Applications to Ligand Design

An extensive comparison of full-QM (B3LYP) and QM/MM (B3LYP:UFF) levels of theory has been made for two enantioselective catalytic systems, namely, Pybox-Ru and Box-Cu complexes, in the cyclopropanation of alkenes (ethylene and styrene) with methyl diazoacetate. The geometries of the key reaction intermediates and transition structures calculated at the QM/MM level are generally in satisfactory agreement with full-QM calculated geometries. More importantly, the relative energies calculated at the QM/MM level are in good agreement with those calculated at the full-QM level in all cases. Furthermore, the QM/MM energies are often in better agreement with the stereoselectivity experimentally observed, and this suggests that QM/MM calculations can be superior to full-QM calculations when subtle differences in inter- and intramolecular interactions are important in determining the selectivity, as is the case in enantioselective catalysis. The predictive value of the model presented is validated by the explanation of the unusual enantioselectivity behavior exhibited by a new bis-oxazoline ligand, the stereogenic centers of which are quaternary carbon atoms.