On the spin and symmetry adaptation of the density matrix renormalization group method

We present a spin-adapted density matrix renormalization group (DMRG) algorithm designed to target spin and spatial symmetry states that can be difficult to obtain while using a non-spin-adapted algorithm. The algorithmic modifications that have to be introduced into the usual density matrix renormalization group scheme in order to spin adapt it are discussed, and it is demonstrated that the introduced modifications do not change the overall scaling of the method. The new approach is tested on HNCO, a model system, that has a singlet-triplet curve crossing between states of the same symmetry. The advantages of the spin-adapted DMRG scheme are discussed, and it is concluded that the spin-adapted DMRG method converges better in almost all cases and gives more parallel curves to the full configuration interaction result than the non-spin-adapted method. It is shown that the spin-adapted DMRG energies can be lower than the ones obtained from the non-spin-adapted scheme. Such a counterintuitive result is explained by noting that the spin-adapted method is not a special case of the non-spin-adapted one; consequently, the spin-adapted result is not an upper bound for the non-spin-adapted energy.     

Overcoming entropic barrier with coupled sampling at dual resolutions

An enhanced sampling method is proposed for ab initio protein folding simulations. The new method couples a high-resolution model for accuracy and a low-resolution model for efficiency. It aims to overcome the entropic barrier found in the exponentially large protein conformational space when a high-resolution model, such as an all-atom molecular mechanics force field, is used. The proposed method is designed to satisfy the detailed balance condition so that the Boltzmann distribution can be generated in all sampling trajectories in both high and low resolutions. The method was tested on model analytical energy functions and ab initio folding simulations of a beta-hairpin peptide. It was found to be more efficient than replica-exchange method that is used as its building block. Analysis with the analytical energy functions shows that the number of energy calculations required to find global minima and to converge mean potential energies is much fewer with the new method. Ergodic measure shows that the new method explores the conformational space more rapidly. We also studied imperfect low-resolution energy models and found that the introduction of errors in low-resolution models does decrease its sampling efficiency. However, a reasonable increase in efficiency is still observed when the global minima of the low-resolution models are in the vicinity of the global minimum basin of the high-resolution model. Finally, our ab initio folding simulation of the tested peptide shows that the new method is able to fold the peptide in a very short simulation time. The structural distribution generated by the new method at the equilibrium portion of the trajectory resembles that in the equilibrium simulation starting from the crystal structure.     

A multivariate method for relating groups of measurements connected by a causal pathway

The multivariate regression model solved by partial least squares, PLS, is extended to more than one predictor block; two algorithms are discussed in detail. The performance of the method is tested by applying it to a water quality problem. Several underlying factors are revealed. Contributions of the various ions are assigned to the different polluting run-offs.     

"Exact" surface free energies of iron surfaces using a modified embedded atom method potential and lambda integration

Previously a new universal lambda-integration path and associated methodology was developed for the calculation of "exact" surface and interfacial free energies of solids. Such a method is in principle applicable to any intermolecular potential function, including those based on ab initio methods, but in previous work the method was only tested using a relatively simple embedded atom method iron potential. In this present work we apply the new methodology to the more sophisticated and more accurate modified embedded atom method (MEAM) iron potential, where application of other free- energy methods would be extremely difficult due to the complex many-body nature of the potential. We demonstrate that the new technique simplifies the process of obtaining "exact" surface free energies by calculating the complete set of these properties for the low index surface faces of bcc and fcc solid iron structures. By combining these data with further calculations of liquid surface tensions we obtain the first complete set of exact surface free energies for the solid and liquid phases of a realistic MEAM model system. We compare these predictions to various experimental and theoretical results.     

Interpolation of multidimensional diabatic potential energy matrices

A method for constructing diabatic potential energy matrices by interpolation of ab initio quantum chemistry data is described and tested. This approach is applicable to any number of interacting electronic states, and relies on a formalism and a computational procedure that are more general than those presented previously for the case of two electronic states. The method is tested against an analytic model for three interacting electronic states of NH(3) (+).     

Microwave-assisted extraction of trichloroethylene from clay samples

A new method for volatile organic compounds (VOCs) extraction from low-permeability media, such as clay, has been developed and tested using trichloroethylene (TCE) as a model compound. The method is based on microwave-assisted extraction (MAE), which uses microwave energy to heat the extracting solvent and the sample. MAE allows the extraction process to be carried out at elevated temperatures and pressures, which dramatically reduces the time required to complete the process. A custom-made PTFE vessel was used for extraction investigations. TCE analysis was performed using gas chromatography with electron capture detection (GC-ECD). Three different solvents were tested: methanol, 1?:?1 hexane?:?acetone mixture, and 10?:?1 hexane?:?acetone mixture. A comparison of TCE recoveries from clay samples using the new method and the standard methanol extraction method was carried out. The newly developed method and the method currently in use were found to recover similar amounts of TCE. The major advantage of the MAE technique is the very short time needed to obtain complete analyte recovery (6–10?min), which makes it possible to analyse a large number of samples without the need for sample preservation or prolonged storage. Thus, the new method is much more efficient than the existing methods. The technique has a good potential for field application.     

On the unphysical impact of complex absorbing potentials on the Hamiltonian and its remedy

The introduction of complex absorbing potentials as numerical tools to stabilize or increase the efficiency of calculations based on wave-packet propagation or on eigenvalue problems has the drawback of causing a modification of the Hamilton operator of the problem. In this work the consequences of such a modification are analyzed and the corrections required in order to properly describe the original physical process are derived. As an example, the decay of excited molecular states is considered: it is shown that the standard time-independent expression for the decay spectrum loses its validity when a complex absorbing potential is introduced in the nuclear Hamilton operator of the problem. To remedy the situation, a new, very stable formula is derived and tested on relevant model studies. Numerical examples are discussed.     

Multiscale modeling of materials based on force and charge density fidelity

The approximate representation of a quantum solid as an equivalent composite semiclassical solid is considered for insulating materials. The composite is comprised of point ions moving on a potential energy surface. In the classical bulk domain this potential energy is represented by potentials constructed to give the same structure and elastic properties as the underlying quantum solid. In a small local quantum domain the potential is determined from a detailed quantum calculation of the electronic structure. The new features of this well-studied problem are (1) a clearly stated theoretical context in which approximations leading to the model are introduced, (2) the representation of the classical domain by potentials focused on reproducing the specific quantum response being studied, (3) development of "pseudoatoms" for a realistic treatment of charge densities where bonds have been broken to define the environment of the quantum domain, and (4) inclusion of polarization effects on the quantum domain due to its distant bulk environment. This formal structure is illustrated in detail for a SiO(2) nanorod. More importantly, each component of the proposed modeling is tested quantitatively for this case, verifying its accuracy as a faithful multiscale model of the original quantum solid. To do so, the charge density of the entire nanorod is calculated quantum mechanically to provide the reference by which to judge the accuracy of the modeling. The construction of the classical potentials, the rod, the pseudoatoms, and the multipoles is discussed and tested in detail. It is then shown that the quantum rod, the rod constructed from the classical potentials, and the composite classical/quantum rod all have the same equilibrium structure and response to elastic strain. In more detail, the charge density and forces in the quantum subdomain are accurately reproduced by the proposed modeling of the environmental effects even for strains beyond the linear domain. The accuracy of the modeling is shown to apply for two quite different choices for the underlying quantum chemical method: transfer Hamiltonian and density functional methods.     

A simulation of the exchange potential in unrestricted and restricted Hartree-Fock calculations studied on atoms

The spherical average of the Hartree-Fock exchange potential depending on each spin orbital is compared with Slater's exchange potential, V _xs, as demonstrated for the phosphorus atom. It is shown that the former potential can be simulated by (a + br)V _xs, where r is the radius and the constants a and b are calculated for each spin orbital. This simulation is tested for the iron atom and it is found that the results agree well with those obtained from unrestricted and restricted Hartree-Fock calculations, respectively. The applicability of this new method in energy band structure calculations is briefly discussed.Dedicated to Professor H. Hartmann on the occasion of his 65th birthday.     

Relation between Electric Spark Sensitivity and Impact Sensitivity of Nitroaromatic Energetic Compounds

Impact and electric spark sensitivities of energetic compounds are two important sensitivity parameters, which are closely related to many accidents in working places. In contrast to electric spark sensitivity, impact sensitivity can be easily measured. A new simple method is introduced to correlate electric spark and impact sensitivities of nitroaromatic compounds. Two correcting functions are used to consider several molecular moieties for reliable prediction of electric spark sensitivity through the measured or estimated impact sensitivity of nitroaromatics. The model is optimized using a set of 28 CHNO polynitroaromatic explosives and then it is tested for some nitroaromatics containing the other atoms such as sulfur. The predicted electric sensitivities of the new method are also compared with the reported results of a new quantum mechanical approach. For 22 CHNO nitroaromatics, quantum mechanical calculations are within ±3.0 J of 18 measured values and more than ±3.0 J for remaining 4 experimental data. Meanwhile, the predicted results of the method are less than ±3.0 J for 28 CHNO nitroaromatics. The root‐mean‐square (rms) deviations of the new model and quantum mechanical are also 1.55 and 2.51 J, respectively.     

Surface tension of a Lennard-Jones liquid under supersaturation

A formally exact Kirkwood-Buff virial formula for the surface tension of a supersaturated interface is derived. A modified Gibbs ensemble method is given that allows the creation of interacting supersaturated phases of equal chemical potential, and which enables the Kirkwood-Buff formula to be applied. The methods are tested by Monte Carlo simulation of a supersaturated Lennard-Jones fluid with a planar liquid-vapor interface. The Kirkwood-Buff results for the supersaturated surface tension are found to be in reasonable agreement with new results obtained here using the recently developed, formally exact, ghost interface method, [M. P. Moody and P. Attard, J. Chem. Phys., 2002, 117, 6705]. The surface tension is obtained as a function of supersaturation at four temperatures, and it is found to decrease with increasing supersaturation, and to vanish at the vapor spinodal. The relevance of the present results to the nucleation of droplets in a supersaturated vapor is discussed.     

New hybrid method for reactive systems from integrating molecular orbital or molecular mechanics methods with analytical potential energy surfaces

A computational approach to calculating potential energy surfaces for reactive systems is presented and tested. This hybrid approach is based on integrated methods where calculations for a small model system are performed by using analytical potential energy surfaces, and for the real system by using molecular orbital or molecular mechanics methods. The method is tested on a hydrogen abstraction reaction by using the variational transition-state theory with multidimensional tunneling corrections. The agreement between the calculated and experimental information depends on the quality of the method chosen for the real system. When the real system is treated by accurate quantum mechanics methods, the rate constants are in excellent agreement with the experimental measurements over a wide temperature range. When the real system is treated by molecular mechanics methods, the results are still good, which is very encouraging since molecular mechanics itself is not at all capable of describing this reactive system. Since no experimental information or additional fits are required to apply this method, it can be used to improve the accuracy of molecular orbital methods or to extend the molecular mechanics method to treat any reactive system with the single constraint of the availability of an analytical potential energy surface that describes the model system.     

Prediction of multicomponent liquid adsorption using excess quantities. II. Calculations for the liquid/solid interface

The utilization of excess quantities as the basis for a thermodynamic approach can simplify the prediction of multicomponent liquid adsorption from binary data. A new method for predicting liquid adsorption on solids is suggested, which is different from the existing equations with respect to the theoretical background and formulation. The applicability of the new model is tested with three ternary adsorption systems. The predicted surface excesses are discussed and compared with experimental ones and with those of other prediction models in the literature. The accordance between measured and predicted ternary data is convincing.     

Protein stability prediction: a Poisson-Boltzmann approach

Most proteins are only marginally stable at physiological temperatures. Thus a common defect due to mutation is the loss of protein stability, resulting in loss of their well-defined structures and functions at their functioning temperatures. Quantification of protein stability change upon mutation has attracted a large number of experimental and theoretical studies. In this work, we have extended the Poisson-Boltzmann theory that is originally used for predicting stability changes of charged mutations to predicting stability changes of all mutations. To achieve this, we have proposed a free energy model covering both electrostatic and hydrophobic interactions. A G?-like model for the denatured state that incorporates both nativeness and randomness of the denatured state has been used to calculate the hydrophobic contribution to protein stability. The new model is computationally simple and fast, and performs well for charged and hydrophobic mutations for all four tested proteins. Future directions for extending the method into pH-dependent effect and more accurate prediction for polar mutations are discussed.     

Orotic acid: a milk constituent Enzymatic determination by means of a new microcalorimetric method

The presence of orotic acid (a precursor of nucleic acid) in milk is very important in order to ensure its nutritional value and good conservation. In the literature, chromatographic, spectrophotometric and polarographic methods are reviewed. The reported values have a very wide interval range (19-664 mg l(-1)) and a low precision. The new method proposed in this article employs an enzymatic reaction. It has been improved on standards and then tested on milk samples. The same samples were also tested by means of a known spectrophotometric method. The new analytical method for orotic acid determination is reliable; the results are more accurate and more precise if compared with the usual methods, and it shows the same sensibility. The calorimetric analysis is faster and easier, owing to the fact that no sample treatments are required.     

Determination of free energy profiles by repository based adaptive umbrella sampling: bridging nonequilibrium and quasiequilibrium simulations

We propose a new adaptive sampling approach to determine free energy profiles with molecular dynamics simulations, which is called as "repository based adaptive umbrella sampling" (RBAUS). Its main idea is that a sampling repository is continuously updated based on the latest simulation data, and the accumulated knowledge and sampling history are then employed to determine whether and how to update the biasing umbrella potential for subsequent simulations. In comparison with other adaptive methods, a unique and attractive feature of the RBAUS approach is that the frequency for updating the biasing potential depends on the sampling history and is adaptively determined on the fly, which makes it possible to smoothly bridge nonequilibrium and quasiequilibrium simulations. The RBAUS method is first tested by simulations on two simple systems: a double well model system with a variety of barriers and the dissociation of a NaCl molecule in water. Its efficiency and applicability are further illustrated in ab initio quantum mechanics/molecular mechanics molecular dynamics simulations of a methyl-transfer reaction in aqueous solution.