Free enthalpy landscape of SrO

Trying to predict thermodynamically stable and metastable solid compounds as function of pressure and temperature requires the global exploration of the enthalpy landscapes of chemical systems and the subsequent construction of their free enthalpy landscapes. In this work, we present a general approach to the determination of a free energy landscape. As an example, we construct the free enthalpy landscape of SrO for two different pressures on the empirical potential level and also compute various thermodynamic and elastic properties of SrO in the NaCl-, CsCl-, NiAs-, NbS-, TiP-, beta-BeO, sphalerite-, and wurtzite-structure type on an ab initio level. We employ density functional theory within the hybrid B3LYP approximation. The results show good agreement with experimental and theoretical data.     

Ab initio and empirical energy landscapes of (MgF2)n clusters (n = 3, 4)

We explore the energy landscape of (MgF(2))(3) on both the empirical and ab initio level using the threshold algorithm. In order to determine the energy landscape and the dynamics of the trimer we investigate not only the stable isomers but also the barriers separating these isomers. Furthermore, we study the probability flows in order to estimate the stability of all the isomers found. We find that there is reasonable qualitative agreement between the ab initio and empirical potential, and important features such as sub-basins and energetic barriers follow similar trends. However, we observe that the energies are systematically different for the less compact clusters, when comparing empirical and ab initio energies. Since the underlying motivation of this work is to identify the possible clusters present in the gas phase during a low-temperature atom beam deposition synthesis of MgF(2), we employ the same procedure to additionally investigate the energy landscape of the tetramer. For this case, however, we use only the empirical potential.     

Global geometry optimization of small silicon clusters at the level of density functional theory

By an application to small silicon clusters Si _N (with N = 4,5,7,10) it is shown that truly global geometry optimization on an ab initio or density functional theory level can be achieved, at a computational cost of approximately 1–5 traditional local optimization runs (depending on cluster size). This extends global optimization from the limited area of empirical potentials into the realm of ab initio quantum chemistry. Received: 24 February 1998 / Accepted: 6 March 1998 / Published online: 17 June 1998     

Ab initio prediction of the low-temperature phase diagrams in the systems KBr-NaBr, KX-RbX, and LiX-RbX (X=Cl,Br)

The authors have calculated the low-temperature phase diagrams for the ternary alkali halides KBr-NaBr, KX-RbX, and LiX-RbX (X=Cl,Br) systems on the ab initio level without any recourse to experimental information. Via global exploration of the enthalpy landscapes for many different compositions in these systems, candidates for both ordered stoichiometric modifications and crystalline solid solution phases have been identified. Next, their free enthalpies were computed on ab initio level, and the respective low-temperature phase diagram has been derived. They find miscibility gaps in the systems KBr-NaBr and KX-RbX (X=Cl,Br), while in LiX-RbX (X=Cl,Br) only crystalline ordered phases should be present, in agreement with available experimental data. Furthermore, they predict several new thermodynamically stable and metastable phases in these systems.     

Low energy structures of gold nanoclusters in the size range 3–38 atoms

Using a combination of first principles calculations and empirical potentials we have undertaken a systematic study of the low energy structures of gold nanoclusters containing from 3 to 38 atoms. A Lennard-Jones and many-body potential have been used in the empirical calculations, while the first principles calculations employ an atomic orbital, density functional technique. For the smaller clusters (n=3–5) the potential energy surface has been mapped at the ab initio level and for larger clusters an empirical potential was first used to identify low energy candidates which were then optimised with full ab initio calculations. At the DFT-LDA level, planar structures persist up to six atoms and are considerably more stable than the cage structures by more than 0.1 eV/atom. The difference in ab initio energy between the most stable planar and cage structures for seven atoms is only 0.04 eV/atom. For larger clusters there are generally a number of minima in the potential energy surface lying very close in energy. Furthermore our calculations do not predict ordered structures for the magic numbers n=13 and 38. They do predict the ordered tetrahedral structure for n=20. The results of the calculations show that gold nanoclusters in this size range are mainly disordered and will likely exist in a range of structures at room temperature.     

Ab initio prediction of the low-temperature phase diagrams in the systems CsX–LiX (X = F, Cl, Br, I)

We have calculated the low-temperature phase diagrams for the ternary alkali halides CsX–LiX (X = F, Cl, Br, I) at an ab initio level without any recourse to experimental information. The starting point of our general approach is the global exploration of the enthalpy landscapes for many different compositions in these systems. Candidates for both ordered stoichiometric modifications and crystalline solid-solution phases are identified, and their free enthalpies are computed at an ab initio level. From this the low-temperature phase diagrams are derived. We find that in all systems under investigation only crystalline ordered phases should be present, in agreement with available experimental data. Furthermore, we predict several new thermodynamically stable and metastable phases in these systems.     

Alternative search strategy for minimal energy nanocluster structures: the case of rhodium, palladium, and silver

An alternative strategy to find the minimal energy structure of nanoclusters is presented and implemented. We use it to determine the structure of metallic clusters. It consists in an unbiased search, with a global minimum algorithm: conformational space annealing. First, we find the minima of a many-body phenomenological potential to create a data bank of putative minima. This procedure assures us the generation of a set of cluster configurations of large diversity. Next, the clusters in this data bank are relaxed by ab initio techniques to obtain their energies and geometrical structures. The scheme is successfully applied to magic number 13 atom clusters of rhodium, palladium, and silver. We obtained minimal energy cluster structures not previously reported, which are different from the phenomenological minima. Moreover, they are not always highly symmetric, thus casting some doubt on the customary biased search scheme, which consists in relaxing with density functional theory global minima chosen among high symmetry structures obtained by means of phenomenological potentials.     

Molecular tailoring approach for geometry optimization of large molecules: energy evaluation and parallelization strategies

A linear-scaling scheme for estimating the electronic energy, gradients, and Hessian of a large molecule at ab initio level of theory based on fragment set cardinality is presented. With this proposition, a general, cardinality-guided molecular tailoring approach (CG-MTA) for ab initio geometry optimization of large molecules is implemented. The method employs energy gradients extracted from fragment wave functions, enabling computations otherwise impractical on PC hardware. Further, the method is readily amenable to large scale coarse-grain parallelization with minimal communication among nodes, resulting in a near-linear speedup. CG-MTA is applied for density-functional-theory-based geometry optimization of a variety of molecules including alpha-tocopherol, taxol, gamma-cyclodextrin, and two conformations of polyglycine. In the tests performed, energy and gradient estimates obtained from CG-MTA during optimization runs show an excellent agreement with those obtained from actual computation. Accuracy of the Hessian obtained employing CG-MTA provides good hope for the application of Hessian-based geometry optimization to large molecules.     

Structure Prediction of Binary Pernitride MN2 Compounds (M=Ca,Sr, Ba,La, and Ti)

Metal‐pernitride compounds belong to a class of chemical systems in which both the complex ions and the non‐bonding electrons may play roles in the formation of their modified crystalline structures. To investigate this issue, the energy landscapes of pernitrides of metals with different maximum valence (M=Ca, Sr, Ba, La, and Ti) were globally explored on the ab initio level at standard and high pressures, thereby yielding possible (meta)stable modifications in these systems together with information on how the landscape changed as function of the valence of the metal cation. For all of the systems in which no compounds had been synthesized so far, we predicted the existence of kinetically stable modifications that should, in principle, be experimentally accessible. In particular, TiN₂ should crystallize in a new structure type, TiN₂‐I.     

Ab initio-based intermolecular carbon-carbon pair potentials for polycyclic aromatic hydrocarbon clusters

We derived the carbon-carbon pair potentials for polycyclic aromatic hydrocarbon (PAH) clusters, which exhibited a strikingly similar geometry to that of the two-layer graphite. The binding energy of PAH clusters ranging in size from the benzene dimer to the pyrene dimer obtained by ab initio calculations at the MP2 level was used to extract the pair potentials in the form of the Lennard-Jones and Exponential-6 functions. Identical binding energy and equilibrium interlayer distance were reproduced by these functions to those calculated by the ab initio method. The pair potentials for PAHs yield the same equilibrium C-C distance as the known pair potentials for graphite and fullerenes, but nearly twice the well depth because of the polarization of the C-H bond.     

First principles predictions of thermophysical properties of refrigerant mixtures

We present pair potentials for fluorinated methanes and their dimers with CO(2) based on ab initio potential energy surfaces. These potentials reproduce the experimental second virial coefficients of the pure fluorinated methanes and their mixtures with CO(2) without adjustment. Ab initio calculations on trimers are used to model the effects of nonadditive dispersion and induction. Simulations using these potentials reproduce the experimental phase-coexistence properties of CH(3)F within 10% over a wide range of temperatures. The phase coexistence curve of the mixture of CH(2)F(2) and CO(2) is reproduced with an error in the mole fractions of both phases of less than 0.1. The potentials described here are based entirely on ab initio calculations, with no empirical fits to improve the agreement with experiment.     

Cis-->trans, trans-->cis isomerizations and N-O bond dissociation of nitrous acid (HONO) on an ab initio potential surface obtained by novelty sampling and feed-forward neural network fitting

The isomerization and dissociation dynamics of HONO are investigated on an ab initio potential surface obtained by fitting the results of electronic structure calculations at 21 584 configurations by using previously described novelty sampling and feed-forward neural network (NN) methods. The electronic structure calculations are executed by using GAUSSIAN 98 with a 6-311G(d) basis set at the MP4(SDQ) level of accuracy. The average absolute error of the NN fits varies from 0.012 eV (1.22 kJ mol(-1)) to 0.017 eV (1.64 kJ mol(-1)). The average computation time for a HONO trajectory using a single NN surface is approximately 4.8 s. These computation times compare very favorably with those required by other methods primarily because the NN fitting needs to be executed only one time rather than at every integration point. If the average result obtained from a committee of NNs is employed at each point rather than a single NN, increased fitting accuracy can be achieved at the expense of increased computational requirements. In the present investigation, we find that a committee comprising five NN potentials reduces the average absolute interpolation error to 0.0111 eV (1.07 kJ mol(-1)). Cis-trans isomerization rates with total energy of 1.70 eV (including zero point energy) have been computed for a variety of different initial distributions of the internal energy. In contrast to results previously reported by using an empirical potential, where cis-->trans to trans-->cis rate coefficient ratios at 1.70 eV total energy were found to lie in the range of 2.0-12.9 depending on the vibration mode excited, these ratios on the ab initio NN potential lie in the range of 0.63-1.94. It is suggested that this result is a reflection of much larger intramode coupling terms present in the ab initio potential surface. A direct consequence of this increased coupling is a significant decrease in the mode specific rate enhancement when compared to results obtained by using empirical surfaces. All isomerizations are found to be first order in accordance with the results reported by using empirical potentials. The dissociation rate to NO+OH has been investigated at internal HONO energies of 3.10 and 3.30 eV for different distributions of this energy among the six vibrational modes of HONO. These dissociations are also found to be first order. The computed dissociation rate coefficients exhibit only modest mode specific rate enhancement that is significantly smaller than that obtained on an empirical surface because of the much larger mode couplings present on the ab initio surface.     

Composition-induced structural transitions in mixed Lennard-Jones clusters: global reparametrization and optimization

As extended benchmarks to global cluster structure optimization methods, we provide a first systematic point of entry into the world of strongly mixed rare gas clusters. A new set of generalized Lennard-Jones pair potentials is generated for this purpose, by fitting them to high-end ab initio reference data. Employing these potentials in our genetic algorithm-based global structure optimization framework, we examined various systems from binary to quinary mixtures of atom types. A central result from this study is that the famous fcc structure for 38 atoms can survive for certain binary mixtures but appears to be prone to collapsing into the dominating icosahedral structure, which we observed upon introduction of one single atom of a ternary type.     

Free energy perturbation study of water dimer dissociation kinetics

An efficient approach is described for using accurate ab initio calculations to determine the rates of elementary condensation and evaporation processes that lead to nucleation of aqueous aerosols. The feasibility of the method is demonstrated in an application to evaporation rates of water dimer at 230 K. The method, known as ABC-FEP (ab initio/classical free energy perturbation), begins with a calculation of the potential of mean force for the dissociation (evaporation) of small water clusters using a molecular dynamics (MD) simulation with a model potential. The free energy perturbation is used to calculate how changing from the model potential to a potential calculated from ab initio methods would alter the potential of mean force. The difference in free energy is the Boltzmann-weighted average of the difference between the ab initio and classical potential energies, with the average taken over a sample of configurations from the MD simulation. In principle, the method does not require a highly accurate model potential, though more accurate potentials require fewer configurations to achieve a small sampling error in the free energy perturbation step. To test the feasibility of obtaining accurate potentials of mean force from ab initio calculations at a modest number of configurations, the free energy perturbation method has been used to correct the errors when some standard models for bulk water (SPC, TIP4P, and TIP4PFQ) are applied to water dimer. To allow a thorough exploration of sampling issues, a highly accurate fit to results of accurate ab initio calculations, known as SAPT-5s, as been used a proxy for the ab initio calculations. It is shown that accurate values for a point on the potential of mean force can be obtained from any of the water models using ab initio calculations at only 50 configurations. Thus, this method allows accurate simulations of small clusters without the need to develop water models specifically for clusters.     

Interaction potentials for Br(-)-Rg (Rg=He-Rn): spectroscopy and transport coefficients

High-level ab initio CCSD(T) calculations are performed in order to obtain accurate interaction potentials for the Br(-) anion interacting with each rare gas (Rg) atom. For the Rg atoms from He to Ar, two approaches are taken. The first one implements a relativistic core potential and an aug-cc-pVQZ basis set for bromine, an aug-cc-pV5Z basis set for Rg, and a set of bond functions placed at the midpoint of the Rg-Br distance. The second one uses the all-electron approximation with aug-cc-pV5Z bases further augmented by an extra diffuse function in each shell. Comparison reveals close similarity between both sets of results, so for Rg atoms from Kr to Rn only the second approach is exploited. Calculated potentials are assessed against the previous empirical, semiempirical, and ab initio potentials, and against available beam scattering data, zero electron kinetic energy spectroscopic data, and various sets of the measured ion mobilities and diffusion coefficients. This multiproperty analysis leads to the conclusion that the present potentials are consistently good for the whole series of Br(-)-Rg pairs over the whole range of internuclear distances covered.     

Mutual orientation of two C60 molecules: an ab initio study

The orientational dependence of the interaction between two C(60) molecules is investigated using ab initio calculations. The binding energy, computed within density functional theory in the local density approximation, is substantially smaller than the one derived from the experimental heat of sublimation of fullerite, which calls into question the nature of inter-C(60) bonding. According to our calculations, the experimentally observed orientation with a C(60) presenting a hexagon-hexagon bond to a pentagonal face of the other C(60) is not really favored. Some other configurations are very close in energy and in fact a pentagon facing a pentagon and a hexagon facing a hexagon-hexagon bond are found to be slightly more favorable situations. Our results are compared to previous ones obtained either with previous empirical intermolecular potentials or to existing ab initio studies of crystalline C(60). In addition, the stacking of C(60) in a crystal and in a decahedral (C(60))(7) cluster is discussed.     

Ab initio computation of low-temperature phase diagrams exhibiting miscibility gaps

A new methodology for the computation of the low-temperature part of phase diagrams without recourse to any experimental information is presented. A central element is a procedure for deciding whether formation of crystalline solid solution phases can take place in the chemical system. Via global exploration of the enthalpy landscapes for many different compositions in the system, candidates for ordered stoichiometric and crystalline solid solution phases are identified. Next, their free enthalpies are computed at ab initio level and a low-temperature phase diagram is derived. As examples, the low-temperature phase diagrams for the ternary alkali halides NaCl/LiCl NaBr/LiBr and NaCl/KCl are presented.     

Interpolated potential energy surfaces: How accurate do the second derivatives have to be?

A global potential energy surface for the water dimer is constructed using the modified Shepard interpolation scheme of Collins et al. According to this interpolation scheme, the energy at an arbitrary geometry is expressed as a weighted sum of Taylor series expansions from neighboring data points, where the energy and derivative data required are obtained from ab initio calculations. For some ab initio methods, errors are introduced into the second derivative matrix, either by numerical differencing of ab initio energies or numerical integration during the ab initio calculation. Therefore, we test the accuracy required of the second derivative data by truncation of the exact second derivatives to a series of approximate second derivatives, and assess the effect on the results of a quantum diffusion Monte Carlo (QDMC) simulation. Our results show that the calculated zero-point energy and wave function histograms converge to within the numerical uncertainty of the QDMC simulation by inclusion of either three significant figures or three decimal places in the second derivatives.