Bond breaking with auxiliary-field quantum Monte Carlo

Bond stretching mimics different levels of electron correlation and provides a challenging test bed for approximate many-body computational methods. Using the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC) method, we examine bond stretching in the well-studied molecules BH and N(2) and in the H(50) chain. To control the sign/phase problem, the phaseless AF QMC method constrains the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. With single Slater determinants from unrestricted Hartree-Fock as trial wave function, the phaseless AF QMC method generally gives better overall accuracy and a more uniform behavior than the coupled cluster CCSD(T) method in mapping the potential-energy curve. In both BH and N(2), we also study the use of multiple-determinant trial wave functions from multiconfiguration self-consistent-field calculations. The increase in computational cost versus the gain in statistical and systematic accuracy are examined. With such trial wave functions, excellent results are obtained across the entire region between equilibrium and the dissociation limit.     

Eliminating spin contamination in auxiliary-field quantum Monte Carlo: realistic potential energy curve of F(2)

The use of an approximate reference state wave function mid R:Phi(r) in electronic many-body methods can break the spin symmetry of Born-Oppenheimer spin-independent Hamiltonians. This can result in significant errors, especially when bonds are stretched or broken. A simple spin-projection method is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations, which yields spin-contamination-free results, even with a spin-contaminated mid R:Phi(r). The method is applied to the difficult F(2) molecule, which is unbound within unrestricted Hartree-Fock (UHF). With a UHF mid R:Phi(r), spin contamination causes large systematic errors and long equilibration times in AFQMC in the intermediate, bond-breaking region. The spin-projection method eliminates these problems and delivers an accurate potential energy curve from equilibrium to the dissociation limit using the UHF mid R:Phi(r). Realistic potential energy curves are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are in excellent agreement with experiment.     

In silico prediction of annihilators for triplet–triplet annihilation upconversion via auxiliary-field quantum Monte Carlo

The energy of the lowest-lying triplet state (T1) relative to the ground and first-excited singlet states (S0, S1) plays a critical role in optical multiexcitonic processes of organic chromophores. Focusing on triplet–triplet annihilation (TTA) upconversion, the S0 to T1 energy gap, known as the triplet energy, is difficult to measure experimentally for most molecules of interest. Ab initio predictions can provide a useful alternative, however low-scaling electronic structure methods such as the Kohn–Sham and time-dependent variants of Density Functional Theory (DFT) rely heavily on the fraction of exact exchange chosen for a given functional, and tend to be unreliable when strong electronic correlation is present. Here, we use auxiliary-field quantum Monte Carlo (AFQMC), a scalable electronic structure method capable of accurately describing even strongly correlated molecules, to predict the triplet energies for a series of candidate annihilators for TTA upconversion, including 9,10 substituted anthracenes and substituted benzothiadiazole (BTD) and benzoselenodiazole (BSeD) compounds. We compare our results to predictions from a number of commonly used DFT functionals, as well as DLPNO-CCSD(T₀), a localized approximation to coupled cluster with singles, doubles, and perturbative triples. Together with S1 estimates from absorption/emission spectra, which are well-reproduced by TD-DFT calculations employing the range-corrected hybrid functional CAM-B3LYP, we provide predictions regarding the thermodynamic feasibility of upconversion by requiring (a) the measured T1 of the sensitizer exceeds that of the calculated T1 of the candidate annihilator, and (b) twice the T1 of the annihilator exceeds its S1 energetic value. We demonstrate a successful example of in silico discovery of a novel annihilator, phenyl-substituted BTD, and present experimental validation via low temperature phosphorescence and the presence of upconverted blue light emission when coupled to a platinum octaethylporphyrin (PtOEP) sensitizer. The BTD framework thus represents a new class of annihilators for TTA upconversion. Its chemical functionalization, guided by the computational tools utilized herein, provides a promising route towards high energy (violet to near-UV) emission.

Electronic structure theories such as AFQMC can accurately predict the low-lying excited state energetics of organic chromophores involved in triplet–triplet annihilation upconversion. A novel class of benzothiadiazole annihilators is discovered.     

The well-tempered protein

Globular proteins are the most functionally versatile class of molecules in the biosphere. They play leading roles in practically every aspect of cell physiology, including gene expression, developmental and metabolic regulation, transport, and catalysis. Essential to a protein's function is its characteristic and geometrically well-defined three-dimensional shape, or native state. Proteins, however, are synthesized by the cell as biologically inactive linear chains; it is only upon folding to their native states that globular proteins come to life. The general principles underlying the behavior of proteins as amphiphilic heteropolymer molecules, as well as those unique properties of proteins as biopolymers that are evolutionarily selected for folding and function are important for understanding globular proteins. Recently, there have been many successes in recent studies of lattice and off-lattice coarse-grained models of proteins, as well as in the main current challenges facing the field. © 1999 Elsevier Science Ltd.     

A study of H+H2 and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with plane wave and Gaussian basis sets

The authors present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H(2) near the equilibrium geometry and in the van der Walls limit, as well as the H(2)O, OH, and H(2)O(2) molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a plane wave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration interaction show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values.     

Reactive Monte Carlo and grand-canonical Monte Carlo simulations of the propene metathesis reaction system

The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.     

Quantum Monte Carlo study of first-row atoms using transcorrelated variational Monte Carlo trial functions

The effect of using the transcorrelated variational Monte Carlo (TC-VMC) approach to construct a trial function for fixed node diffusion Monte Carlo (DMC) energy calculations has been investigated for the first-row atoms, Li to Ne. The computed energies are compared with fixed node DMC energies obtained using trial functions constructed from Hartree-Fock and density functional levels of theory. Despite major VMC energy improvement with TC-VMC trial functions, no improvement in DMC energy was observed using these trial functions for the first-row atoms studied. The implications of these results on the nodes of the trial wave functions are discussed.     

Delayed rejection variational Monte Carlo

An acceleration algorithm to address the problem of multiple time scales in variational Monte Carlo simulations is presented. After a first attempted move has been rejected, the delayed rejection algorithm attempts a second move with a smaller time step, so that even moves of the core electrons can be accepted. Results on Be and Ne atoms as test cases are presented. Correlation time and both average accepted displacement and acceptance ratio as a function of the distance from the nucleus evidence the efficiency of the proposed algorithm in dealing with the multiple time scales problem.     

Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.     

Boltzmann bias grand canonical Monte Carlo

We derive an efficient method for the insertion of structured particles in grand canonical Monte Carlo simulations of adsorption in very confining geometries. We extend this method to path integral simulations and use it to calculate the isotherm of adsorption of hydrogen isotopes in narrow carbon nanotubes (two-dimensional confinement) and slit pores (one-dimensional confinement) at the temperatures of 20 and 77 K, discussing its efficiency by comparison to the standard path integral grand canonical Monte Carlo algorithm. We use this algorithm to perform multicomponent simulations in order to calculate the hydrogen isotope selectivity for adsorption in narrow carbon nanotubes and slit pores at finite pressures. The algorithm described here can be applied to the study of adsorption of real oligomers and polymers in narrow pores and channels.     

Monte Carlo studies of tethered chains

Monte Carlo computer simulations of end-tethered chains grafted onto a hard wall have been performed. The chains were modeled as self-avoiding chains on a cubic lattice at athermal solvent conditions. The simulations spanned a wide range of chain lengths, N (100–1000, i.e., up to molecular weights of a few hundred thousands), and anchoring densities, σ (2 × 10⁻⁴ to 0.4), to properly chart the relevant parameter space. It is shown that the reduced surface coverage σ* = σπR is the most appropriate variable that quantitatively determines the mushroom, overlapping mushroom and brush regimes, where R_g is the radius of gyration of a free chain in solution. The simulation data are analyzed to determine the conformational characteristics and shape of the anchored chains and to compare them with the predictions of the analytical self consistent field theory. The strong stretching limit of the theoretical predictions is obtained only for σ* > 8. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47:2449–2461, 2009     

Prospects for release-node quantum Monte Carlo

We perform release-node quantum Monte Carlo simulations on the first row diatomic molecules in order to assess how accurately their ground-state energies can be obtained. An analysis of the fermion-boson energy difference is shown to be strongly dependent on the nuclear charge, Z, which in turn determines the growth of variance of the release-node energy. It is possible to use maximum entropy analysis to extrapolate to ground-state energies only for the low Z elements. For the higher Z dimers beyond boron, the error growth is too large to allow accurate data for long enough imaginary times. Within the limit of our statistics we were able to estimate, in atomic units, the ground-state energy of Li(2) (-14.9947(1)), Be(2) (-29.3367(7)), and B(2)(-49.410(2)).     

Monte Carlo simulation of DNA electrophoresis

This paper describes an attempt to study the electrophoresis mobility of a DNA molecule in a gel by means of a Monte Carlo simulation. We find that the electrophoresis mobility mu can be well described by the empirical equation mu v kappa 1/N + kappa 2E2 with N being the number of monomers of the model chain and E being the applied field. For small E the data can merge into the linear response result mu = kappa 1/N. The paper also discusses necessary extensions of the present approach.     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

Monte Carlo simulation of polymer welding

Monte Carlo Modelling of random polymer chains, course grained onto a cubic F lattice, provides the ability to monitor the long range relaxation processes and the dynamic parameters of chains up to 400 units long. The model, described and verified by Haire et al. (Haire KR, Carver TJ, Windle AH. A Monte Carlo model for dense polymer systems and its interlocking with molecular dynamics simulation. Computational and Theoretical Polymer Science 2000; in press), is here applied to the study of molecular parameters in the vicinity of different types of surface and also to the process of polymer welding, whereby adhesion between two adjacent surfaces is achieved by the interpenetration of chains which are across the surface.The model demonstrates that a surface distorts the conformation of chains adjacent to it to give an oblate molecular envelope, that the concentration of vacant sites and chain ends increases near to the surface and that the density of points representing the centres of mass of the chains increases in the sub-surface regions. These results confirm earlier predictions and provide additional confidence in the model.Modelling of the welding process leads to the parameter intrinsic weld time, t_w, which is the time from initial perfect contact of the surfaces to the achievement of a weld within which the chain conformation is indistinguishable from the bulk. After the initial period in which the mating surfaces roughen, the welding proceeds according to the t^1/4 law predicted by reptation theory. The time to a given level of interdiffusion across the boundary is proportional to the chain length l, a comparatively weak dependence, while t_w is proportional to l³, a strong dependence. This is the same dependence on length as for the relaxation time of the chain end-to-end vectors. In fact, the agreement between the relaxation time, measured on the model of the bulk, and t_w is surprisingly close, at least for the monodisperse polymers investigated here.     

Monte Carlo correction programme for PC

A Monte Carlo correction program for quantitative microanalysis on PC computer is introduced in this paper. The elastic scattering is described by the screened Rutherford cross section. Instead of computing the energy loss according to the actual path between two scatterings we have defined the Bethe inelastic cross section determined by the Bethe-slowing-down approximation. It is assumed that it causes no angular departure of the scattered electron. In the second model we took into account the angular dependence of inelastic scattering assuming that the primary electron interacts with quasi-free atom electrons. On the basis of these two models analytical Monte Carlo programmes were developed and experimentally tested on some oxide glass. Our results are fully comparable to those obtained by ten world microprobe laboratories using classical ZAF correction or Bence-Albee methods. We have found that introducing angular part of the inelastic cross section analytical results did not significantly change. All of our results were carried out for bulk specimens but extending it to layers is under the development.     

Monte Carlo simulation of osmotic equilibria

We present a Metropolis Monte Carlo simulation algorithm for the Tpπ-ensemble, where T is the temperature, p is the overall external pressure, and π is the osmotic pressure across the membrane. The algorithm, which can be applied to small molecules or sorption of small molecules in polymer networks, is tested for the case of Lennard-Jones interactions.     

表面扩散的Monte Carlo初探

利用ＭｏｎｔｅＣａｒｌｏ方法模拟了理想表面和分形表面上的扩散过程；通过模拟可以发现，表面扩散系数不仅与表面浓度有关，而且还与扩散的时间、表面的几何形貌等有关。在表面覆盖度比较高时，表面扩散系数有一极大值。与理想表面相比，分形表面会使扩散系数减小。     

自优化扩散量子Monte Carlo差值法

提出了自优化扩散量子MonteCarlo差值法,这是一个集优化、扩散和相关取样三项技术于一身的MonteCarlo新算法.这个算法能够在扩散过程中直接计算两个体系之间的能量差,且使计算结果的统计误差达到10^-5hartree数量级,获得相关能达80%以上.应用该方法研究分子势能面,使用"刚性移动"模型,利用Jacobi变换使分子两个几何构型的能量计算具有很好的正相关性,因而能得到准确的能量差值和分子势能面.另外,我们还首创了"平衡后留样"技术,可节省50%以上的计算量.该算法还可应用于分子光谱、化学反应能量变化值等领域的研究.