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Journal ArticleDOI

Ab initio molecular dynamics study of antimony clusters

22 Jun 1995-Journal of Chemical Physics (American Institute of Physics)-Vol. 102, Iss: 24, pp 9631-9637

AbstractWe present an ab initio molecular dynamics study of the atomic and electronic structure of SbN (N=2–8 and 12) clusters within the local density approximation and pseudopotential representation of the electron–ion interaction. Simulated annealing calculations have been done for 6‐, 7‐, 8‐, and 12‐atom clusters. While for Sb4 a bent rhombus is about 2 eV higher in energy than a regular tetrahedron, we find that it plays an important role in the structure of larger clusters. For Sb8 we obtain two weakly interacting tetrahedra to be of lowest energy. However, this is nearly degenerate with a bent rhombus interacting with a distorted tetrahedron. Further, our calculations suggest a bent rhombus based structure for Sb12 cluster indicating the observation of Sb4n clusters in Sb vapor condensation cell to be due to abundance of Sb4 clusters. A large gap is found to exist between the highest and the next occupied Kohn–Sham eigenvalues of the lowest energy isomers of 3‐, 5‐, and 7‐atom clusters. This is in agreemen... more

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Abstract: This review is addressed to colleagues working in different fields of physics who are interested in the concepts of microcanonical thermodynamics, its relation and contrast to ordinary, canonical or grandcanonical thermodynamics, and to get a first taste of the wide area of new applications of thermodynamical concepts like hot nuclei, hot atomic clusters and gravitating systems. Microcanonical thermodynamics describes how the volume of the N-body phase space depends on the globally conserved quantities like energy, angular momentum, mass, charge, etc. Due to these constraints the microcanonical ensemble can behave quite differently from the conventional, canonical or grandcanonical ensemble in many important physical systems. Microcanonical systems become inhomogeneous at first-order phase transitions, or with rising energy, or with external or internal long-range forces like Coulomb, centrifugal or gravitational forces. Thus, fragmentation of the system into a spatially inhomogeneous distribution of various regions of different densities and/or of different phases is a genuine characteristic of the microcanonical ensemble. In these cases which are realized by the majority of realistic systems in nature, the microcanonical approach is the natural statistical description. We investigate this most fundamental form of thermodynamics in four different nontrivial physical cases: 1. (I) Microcanonical phase transitions of first and second order are studied within the Potts model. The total energy per particle is a nonfluctuating order parameter which controls the phase which the system is in. In contrast to the canonical form the microcanonical ensemble allows to tune the system continuously from one phase to the other through the region of coexisting phases by changing the energy smoothly. The configurations of coexisting phases carry important informations about the nature of the phase transition. This is more remarkable as the canonical ensemble is blind against these configurations. It is shown that the three basic quantities which specify a phase transition of first order — Transition temperature, latent heat, and interphase surface entropy — can be well determined for finite systems from the caloric equation of state T(E) in the coexistence region. Their values are already for a lattice of only ~ 30 ∗ 30 spins close to the ones of the corresponding infinite system. The significance of the backbending of the caloric equation of state T(E) is clarified. It is the signal for a phase transition of first order in a finite isolated system. 2. (II) Fragmentation is shown to be a specific and generic phase transition of finite systems. The caloric equation of state T(E) for hot nuclei is calculated. The phase transition towards fragmentation can unambiguously be identified by the anomalies in T(E). As microcanonical thermodynamics is a full N-body theory it determines all many-body correlations as well. Consequently, various statistical multi-fragment correlations are investigated which give insight into the details of the equilibration mechanism. 3. (III) Fragmentation of neutral and multiply charged atomic clusters is the next example of a realistic application of microcanonical thermodynamics. Our simulation method, microcanonical Metropolis Monte Carlo, combines the explicit microscopic treatment of the fragmentational degrees of freedom with the implicit treatment of the internal degrees of freedom of the fragments described by the experimental bulk specific heat. This micro-macro approach allows us to study the fragmentation of also larger fragments. Characteristic details of the fission of multiply charged metal clusters find their explanation by the different bulk properties. 4. (IV) Finally, the fragmentation of strongly rotating nuclei is discussed as an example for a microcanonical ensemble under the action of a two-dimensional repulsive force.

226 citations

Journal ArticleDOI
Abstract: The electronic structure and chemical bonding of the pentapnictogen cluster anions, Pn5- (Pn = P, As, Sb, and Bi), were investigated using both photoelectron spectroscopy and ab initio calculations. Well-resolved photoelectron spectra were obtained for the anions at several photon energies and were analyzed according to the theoretical calculations. The ground state of all the Pn5- species was found to be the aromatic cyclic D5h structure with a C2v low-lying isomer. We found that the C2v isomer gains stability from P5- to Sb5-, consistent with the experimental observation of the coexistence of both isomers in the spectra of Sb5-. The valence molecular orbitals (MOs) of the D5h Pn5- were analyzed and compared to those of the aromatic C5H5- hydrocarbon. The same set of π-MOs is shown to be occupied in the D5h Pn5- and C5H5- species, except that the MO ordering is slightly different. Whereas the three π-MOs in C5H5- all lie above the σ-MOs, the third π orbital (1a2‘ ‘ in Pn5-) lies below the σ-MOs. The stab...

84 citations

Journal ArticleDOI
TL;DR: The first ab initio theoretical study of tetraantimony hexoxide (Sb4O6) is reported, and correction factors for the calculated vibrational frequencies were determined and compared.
Abstract: The first ab initio theoretical study of tetraantimony hexoxide (Sb4O6) is reported. The normal mode frequencies, intensities, and the corresponding vibrational assignments of Sb4O6 in T(d) symmetry were calculated using the GAUSSIAN 98 set of quantum chemistry codes at the Hartree-Fock (HF)/CEP-121G, Moller-Plesset (MP2)/CEP-121G, and density functional theory (DFT)/B3LYP/CEP-121G levels of theory. By comparison to experimental data deduced by our laboratory and others, correction factors for the calculated vibrational frequencies were determined and compared. Normal modes were decomposed into three non-redundant motions (Sb-O-Sb stretch, Sb-O-Sb bend, and Sb-O-Sb wag). Percent relative errors found for the HF, DFT, and MP2 corrected frequencies when compared to experiment are 5.8, 6.1, and 5.7 cm(-1), respectively. Electron distributions for selected molecular orbitals are also considered.

45 citations

Journal ArticleDOI
Abstract: The volume W of the accessible N-body phase space and its dependence on the total energy is directly calculated. The famous Boltzmann relation S = k * ln(W) defines microcanonical thermodynamics (MT). We study how phase transitions appear in MT. Here we first develop the thermodynamics of microcanonical phase transitions of first and second order in systems which are thermodynamically stable in the sense of van Hove. We show how both kinds of phase transitions can unambiguously be identified in relatively small isolated systems of ∼ 100 atoms by the shape of the microcanonical caloric equation of state 〈 T(E/N) ⌨ and not so well by the coexistence of two spatially clearly separated phases. I.e. within microcanonical thermodynamics one does not need to go to the thermodynamic limit in order to identify phase transitions. In contrast to ordinary (canonical) thermodynamics of the bulk microcanonical thermodynamics (MT) gives an insight into the coexistence region. Here the form of the specific heat c(E/N) connects transitions of first and second order in a natural way. The essential three parameters which identify the transition to be of first order, the transition temperature T tr, the latent heat q lat, and the interphase surface entropy Δs ssurf can very well be determined in relatively small systems like clusters by MT. It turns out to be essential whether the cluster is studied canonically at constant temperature or microcanonically at constant energy. Especially the study of phase separations like solid and liquid or, as studied here, liquid and gas is very natural in the microcanonical ensemble, whereas phase separations become exponentially suppressed within the canonical description. The phase transition towards fragmentation is introduced. The general features of MT as applied to the fragmentation of atomic clusters are discussed. The similarities and differences to the boiling of macrosystems are pointed out.

23 citations

Journal ArticleDOI
Abstract: The geometries and vibrational properties of the low-lying electronic states of neutral and anionic of M3 (M = P, As, Sb, and Bi) are studied using the coupled-cluster singles, doubles, and noniterative triples (CCSD(T)) method as well as the density functional theory (B3LYP-DFT) method. For P3-, the and states are almost degenerate. The state, however, turns out to be the lowest state for As3-, Sb3-, and Bi3-, and the adiabatic excitation energies of the state are 0.6, 0.9, and 1.0 eV, respectively. In the anionic trimers of all four elements, another singlet state, 1A1(C2v), is located about 0.3−0.4 eV above ; the energy gap between these states is compared to the splittings between the first two peaks in the photoelectron spectra of these anions. For all of the neutral trimers, the adiabatic and vertical energetic splittings between the Jahn−Teller components of the X2E‘ ‘ and 4E‘ states are calculated to be only 0.04−0.08 eV. Another quartet state, is 0.4 eV higher, almost equal, 0.2 eV lower, and 0.3...

19 citations

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Abstract: The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

14,881 citations

01 Jun 1992

13,084 citations

Journal ArticleDOI
Abstract: An exact stochastic simulation of the Schroedinger equation for charged Bosons and Fermions was used to calculate the correlation energies, to locate the transitions to their respective crystal phases at zero temperature within 10%, and to establish the stability at intermediate densities of a ferromagnetic fluid of electrons.

10,168 citations

Journal Article
Abstract: ., • ' % . ^ : K ~* B J£L~i0813_ 4JC-4 J NATIONAL RESOURCE FOR COMPUTATION IN CHEMISTRY^ '• • ' THE 81R0UND STATED 6|/THE ELECTION A - - .A r >'--H .1 ,4- v c ' M \>~ r tAWRfctftE BERKELEY LABORATORY «r National

9,094 citations

Journal ArticleDOI
Abstract: We present a unified scheme that, by combining molecular dynamics and density-functional theory, profoundly extends the range of both concepts. Our approach extends molecular dynamics beyond the usual pair-potential approximation, thereby making possible the simulation of both covalently bonded and metallic systems. In addition it permits the application of density-functional theory to much larger systems than previously feasible. The new technique is demonstrated by the calculation of some static and dynamic properties of crystalline silicon within a self-consistent pseudopotential framework.

8,457 citations