Optimized Wang-Landau sampling of lattice polymers: Ground state search and folding thermodynamics of HP model proteins

Coarse-grained (lattice-) models have a long tradition in aiding efforts to decipher the physical or biological complexity of proteins. Despite the simplicity of these models, however, numerical simulations are often computationally very demanding and the quest for efficient algorithms is as old as the models themselves. Expanding on our previous work [T. Wu?st and D. P. Landau, Phys. Rev. Lett. 102, 178101 (2009)], we present a complete picture of a Monte Carlo method based on Wang-Landau sampling in combination with efficient trial moves (pull, bond-rebridging, and pivot moves) which is particularly suited to the study of models such as the hydrophobic-polar (HP) lattice model of protein folding. With this generic and fully blind Monte Carlo procedure, all currently known putative ground states for the most difficult benchmark HP sequences could be found. For most sequences we could also determine the entire energy density of states and, together with suitably designed structural observables, explore the thermodynamics and intricate folding behavior in the virtually inaccessible low-temperature regime. We analyze the differences between random and protein-like heteropolymers for sequence lengths up to 500 residues. Our approach is powerful both in terms of robustness and speed, yet flexible and simple enough for the study of many related problems in protein folding.     

Computational methods in coupled electron-ion Monte Carlo simulations.

In the last few years, we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born-Oppenheimer approximation: the coupled electron-ion Monte Carlo method (CEIMC). Electronic properties in CEIMC are computed by quantum Monte Carlo rather than by density functional theory (DFT) based techniques. CEIMC can, in principle, overcome some of the limitations of the present DFT-based ab initio dynamical methods. The new method has recently been applied to high-pressure metallic hydrogen. Herein, we present a new sampling algorithm that we have developed in the framework of the reptation quantum Monte Carlo method chosen to sample the electronic degrees of freedom, thereby improving its efficiency. Moreover, we show herein that, at least for the case of metallic hydrogen, variational estimates of the electronic energies lead to an accurate sampling of the proton degrees of freedom.     

Theoretical modeling of ionization energies of argon clusters: nuclear delocalization effects

Temperature dependence of vertical ionization energies is modeled for small argon clusters (N ≤ 13) using classical parallel-tempering Monte Carlo methods and extended interaction models based on the diatomics-in-molecules approach. Quantum effects at the zero temperature are also discussed in terms of zero-point nuclear vibrations, either at the harmonic approximation level or at the fully anharmonic level using the diffusion Monte Carlo calculations. Both approaches lead to a considerable improvement of the theoretical predictions of argon clusters ionization energies and represent a realistic way of modeling of ionization energies for weakly bound and floppy complexes in general. A thorough comparison with a recent electron-impact experiment [O. Echt et al., J. Chem. Phys. 123, 084313 (2005)] is presented and a novel interpretation of the experimental data is proposed.     

SARS病毒E蛋白的计算机模拟的初步研究

以粗粒化的多肽链模型进行了SARS病毒包膜中E蛋白的计算机模拟,描述了该蛋白质空间构象的概貌.首先扩展了多肽链的HP模型,使之能够用于研究在水或脂环境下蛋白质折叠的行为,并且考虑了全部氨基酸残基疏水相互作用能的差异.相关格子链的MonteCarlo模拟显示了很高的计算效率.模拟再现了蛋白质的coil-globule转变,验证了蛋白质序列分布的重要性.结果表明,在水环境中,E蛋白质空间结构由紧致的疏水内核和部分向外延伸的亲水片段组成;在脂环境中,中部疏水片段会成为向外延伸的环,而当两侧紧致的亲水片段分开时,则形成桥.     

Energies of the first row atoms from quantum Monte Carlo

All-electron variational and diffusion quantum Monte Carlo calculations of the ground state energies of the first row atoms (from Li to Ne) are reported. The authors use trial wave functions of four types: single-determinant Slater-Jastrow wave functions, multideterminant Slater-Jastrow wave functions, single-determinant Slater-Jastrow wave functions with backflow transformations, and multideterminant Slater-Jastrow wave functions with backflow transformations. At the diffusion quantum Monte Carlo level and using their multideterminant Slater-Jastrow wave functions with backflow transformations, they recover 99% or more of the correlation energies for Li, Be, B, C, N, and Ne, 97% for O, and 98% for F.     

Approaching chemical accuracy with quantum Monte Carlo

A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.     

The accuracy of diffusion quantum Monte Carlo simulations in the determination of molecular equilibrium structures

For a test set of 17 first-row small molecules, the equilibrium structures are calculated with Ornstein-Uhlenbeck diffusion quantum Monte Carlo simulations guiding by trial wave functions constructed from floating spherical Gaussian orbitals and spherical Gaussian geminals. To measure performance of the Monte Carlo calculations, the mean deviation, the mean absolute deviation, the maximum absolute deviation, and the standard deviation of Monte Carlo calculated equilibrium structures with respect to empirical equilibrium structures are given. This approach is found to yield results having a uniformly high quality, being consistent with empirical equilibrium structures and surpassing calculated values from the coupled cluster model with single, double, and noniterative triple excitations [CCSD(T)] with the basis sets of cc-pCVQZ and cc-pVQZ. The nonrelativistic equilibrium atomization energies are also presented to assess performance of the calculated methods. The mean absolute deviations regarding experimental atomization energy are 0.16 and 0.21 kcal/mol for the Monte Carlo and CCSD(T)/cc-pCV(56)Z calculations, respectively.     

A study of nucleic acid base-stacking by the Monte Carlo method: Extended cluster approach

The adenine-thymine (AT), adenine-uracil (AU) and guanine-cytosine (GC) base associates in clusters containing 400 water molecules were studied using a newly implemented Metropolis Monte Carlo algorithm based on the extended cluster approach. Starting from the hydrogen-bonded Watson-Crick geometries, all three base pairs are transformed into more favorable stacked configurations during the simulation. The obtained results show, for the first time, the transition from planar base pairs to stacked base associates in the Monte Carlo framework. Analysis of the interaction energies shows that, in the water cluster, the stacked dimers are energetically preferable compared to the corresponding Watson-Crick base pairs. This is due to the larger base-water interaction in the stacked structures. The water-water interaction is one of the main factors promoting the formation of stacked dimers, and the obtained data confirm the crucial role of the water-water interactions in base stacking.     

Calculation of free energies and chemical potentials for gas hydrates using Monte Carlo simulations

We describe a method for calculating free energies and chemical potentials for molecular models of gas hydrate systems using Monte Carlo simulations. The method has two components: (i) thermodynamic integration to obtain the water and guest molecule chemical potentials as functions of the hydrate occupancy; (ii) calculation of the free energy of the zero-occupancy hydrate system using thermodynamic integration from an Einstein crystal reference state. The approach is applicable to any classical molecular model of a hydrate. We illustrate the methodology with an application to the structure-I methane hydrate using two molecular models. Results from the method are also used to assess approximations in the van der Waals-Platteeuw theory and some of its extensions. It is shown that the success of the van der Waals-Platteeuw theory is in part due to a cancellation of the error arising from the assumption of a fixed configuration of water molecules in the hydrate framework with that arising from the neglect of methane-methane interactions.     

用变分Monte Carlo方法处理分子

对变分量子Ｍｏｎｔｅ Ｃａｒｔｏ方法提出了一种种算法：将传统的Ｈａｒｔｒｅｅ－Ｆｏｅｋ方法与量子Ｍｏｎｔｅ Ｃａｒｌｏ方法有机结合在一起；导出了“局部能”的解析式；使用了一种新的相关函数和随机数发生器。我们用这个新算法计算了Ｈ２、ＬｉＨ、Ｌｉ２、Ｈ２Ｏ、Ｆ２分子的基态和ＣＨ２分子的＾３Ｂ１、＾１Ａ１态的能量。计算结果表明，这个新算法在精度和统计误差两个方面比一般ＶＭＣ过程都要好得多。     

Molecular dynamics simulation with stochastically constrained pressure

The authors propose a new algorithm for molecular dynamics simulation. The method includes a Monte Carlo scheme for incrementing the dilation rate in the equations of motion. The new algorithm needs no extra computation and the dynamics of the system preserves its continuity. Application of this approach is very advantageous for models where the derivation and the computation of the pressure is time consuming. The authors present results of model calculations.     

Conformation‐Dependent Sequence Design of HP Copolymers: An Algorithm Based on Sequential Modifications of Monomer Units

We present a new modification of the so‐called conformation‐dependent sequence design scheme for HP copolymers which was proposed several years ago (H and P refer to the hydrophobic and polar monomer units, respectively). New method models the real chemical experiments more realistically. We performed Monte Carlo computer simulations using the bond‐fluctuation model for protein‐like copolymers obtained by means of the new “iterative” method and compared the results with those obtained for originally proposed “instantaneous coloring” procedure. Copolymers designed by the “iterative” method are shown to have better‐optimized functional properties. The investigation of the influence of sequence preparation conditions has revealed that the statistical properties of designed HP sequences depend rather strongly on the density of the parent homopolymer globule but not on the composition of H and P units.     

The lithium-thiophene riddle revisited

A recent study of the interaction of a lithium atom with the thiophene molecule found a large disagreement between high-level coupled cluster (CCSD(T)/AVTZ) and quantum Monte Carlo (fixed-node diffusion Monte Carlo, or FNDMC) calculations. We address this "lithium-thiophene riddle" by analyzing the influence of crucial FNDMC simulation parameters, namely, the one-electron models, basis sets, and pseudopotentials used for the generation of the trial wave function. These are shown to have a significant impact on the calculated FNDMC interaction energies, and good agreement between CCSD(T) and FNDMC is found when nodal hypersurfaces of sufficient quality are used. On the basis of our proposed consensus reference value, we go on to benchmark the standard toolbox of lower-level quantum chemistry methods for this model interaction. Newly developed dispersion-corrected DFT methods perform reasonably well despite the partial charge transfer character of the interaction and might well be worthy of further study in larger lithium-thiophene systems.     

Improved interaction potentials for charged residues in proteins

Electrostatic interactions dominate the structure and free energy of biomolecules. To obtain accurate free energies involving charged groups from molecular simulations, OPLS-AA parameters have been reoptimized using Monte Carlo free energy perturbation. New parameters fit a self-consistent, experimental set of hydration free energies for acetate (Asp), propionate (Glu), 4-methylimidazolium (Hip), n-butylammonium (Lys), and n-propylguanidinium (Arg), all resembling charged residue side chains, including beta-carbons. It is shown that OPLS-AA free energies depend critically on the type of water model, TIP4P or TIP3P; i.e., each water model requires specific water-charged molecule interaction potentials. New models (models 1 and 3) are thus described for both water models. Uncertainties in relative free energies of charged residues are approximately 2 kcal/mol with the new parameters, due to variations in system setup (MAEs of ca. 1 kcal/mol) and noise from simulations (ca. 1 kcal/mol). The latter error of approximately 1 kcal/mol contrasts MAEs from standard OPLS-AA of up to 13 kcal/mol for the entire series of charged residues or up to 5 kcal/mol for the cationic series Lys, Arg, and Hip. The new parameters can be used directly in molecular simulations with no modification of neutral residues needed and are envisioned to be particular important in simulations where charged residues change environment.     

Diffusion Monte Carlo Calculations of Zero-Point Energies of Methanol and Deuterated Methanol

Diffusion Monte Carlo (DMC) simulations have been used to obtain quantum zero-point energies of methanol and all its isotopologs and isotopomers, using a new, accurate semi-global potential energy surface. This potential energy surface is a precise, permutationally invariant fit to 6676 ab initio energies, obtained at the CCSD(T)-F12b/aug-cc-pVDZ level of theory. Quantum zero-point energies of deuterated methanol isotopomers are very close to each other and so a simple statistical argument can be used to estimate the populations of each isotopomer at very low-temperatures. The DMC simulations also indicate that there is virtually zero probability for H/D exchange in the zero-point state. © 2019 Wiley Periodicals, Inc.     

A ground state potential energy surface for H2 using Monte Carlo methods

Using variational Monte Carlo and a simple explicitly correlated wave function we have computed the Born-Oppenheimer energy of the H2 ground state (X 1Sigmag+) at 24 internuclear distances. We have also calculated the diagonal correction to the Born-Oppenheimer approximation and the lowest-order relativistic corrections at each distance using variational Monte Carlo techniques. The nonadiabatic values are evaluated from numerical derivatives of the wave function with respect to the nuclear coordinates. With this potential energy surface we have computed several of the lowest vibrational-rotational energies for this system. Our results are in good agreement with the best values found in the literature.     

The nature of base stacking: a Monte Carlo study

To elucidate the physical origin of the preference of nucleic acid bases for stacking over hydrogen bonding in water, Monte Carlo simulations were performed starting from Watson?CCrick structures of the adenine?Cthymine, adenine?Curacil and guanine?Ccytosine base pairs, as well as from the Hoogsteen adenine?Cthymine base pair, in clusters comprising 400 and 800 water molecules. The simulations employed a newly implemented Metropolis Monte Carlo algorithm based on the extended cluster approach. All simulations reached stacked structures, confirming that such structures are preferred over the hydrogen-bonded Watson?CCrick and Hoogsteen base pairs. The Monte Carlo simulations show the complete transition from hydrogen-bonded base pairs to stacked structures in the Monte Carlo framework. Analysis of the average energies shows that the preference of stacked over hydrogen-bonded structures is due to the increased water?Cbase interaction in these structures. This is corroborated by the increased number of water?Cbase hydrogen bonds in the stacked structures.     

Quantum mechanical single molecule partition function from path integral Monte Carlo simulations

An algorithm for calculating the partition function of a molecule with the path integral Monte Carlo method is presented. Staged thermodynamic perturbation with respect to a reference harmonic potential is utilized to evaluate the ratio of partition functions. Parallel tempering and a new Monte Carlo estimator for the ratio of partition functions are implemented here to achieve well converged simulations that give an accuracy of 0.04 kcal/mol in the reported free energies. The method is applied to various test systems, including a catalytic system composed of 18 atoms. Absolute free energies calculated by this method lead to corrections as large as 2.6 kcal/mol at 300 K for some of the examples presented.     

Path integral ground state study of finite-size systems: application to small (parahydrogen)N (N=2-20) clusters

We use the path integral ground state method to study the energetic and structural properties of small para-H2 clusters of sizes ranging from 2 to 20 molecules. A fourth order formula is used to approximate the short imaginary-time propagator and two interaction potentials are considered. Our results are compared to those of exact basis set calculations and other quantum Monte Carlo methods when available. We find that for all cluster sizes considered, our results show a lower ground state energy than literature values obtained by diffusion Monte Carlo and variational Monte Carlo. For the dimer and trimer, ground state energies are in good agreement with exact results obtained using the discrete variable representation. Structural properties are found to be insensitive to the choice of interaction potential. We explore the use of Pekeris coordinates to analyze the importance of linear arrangement in trimers and for trimers within clusters of larger size.     

Monte Carlo and UBI–QEP Modeling of the Coverage-Dependent Binding Energy for Atomic Adsorbates on the (111) and (100) Transition Metal Surfaces

Using the unity bond index–quadratic exponential potential (UBI–QEP) formalism and the Monte Carlo method, functions are obtained that describe the dependence of the binding energies of atomic adsorbates on the single crystal surface coverage for the models of random adsorption, models with a site choice and site preference, models with neighbor exclusion, and models with diffusion assistance.