Density Functional Study on Structures and Relative Stability of Gd（H2O）n^3＋ （n=8,9）

Density functional theory calculations were performed to study the structures and relative stability of the gadolinium complexes, Gd（H2O）n^3＋ （n=8,9）, in vacuo and in aqueous solution. The polarizable continuum model with various radii for the solute cavity was used to study the relative stability in aqueous solution. The calculated molecular geometries for n=8 and 9 obtained in vacuo are consistent with those observed in experiments. It was found that while the nona-aqua complex is favored in the gas phase, in aqueous solution the octa-aqua conformation is preferred. This result, independent of the types of cavities employed, is in agreement with the experimental observation. The reliability of the present calculation was also addressed by comparing the calculated and experimental free energy of hydration, which revealed that the UA0, UAHF, and UAKS cavities are most appropriate when only the first solvation shell is treated explicitly.

Studies of Thermodynamic Properties and Relative Stability of Polybrominated Xanthones by Density Functional Theory

The thermodynamic properties of xanthone（XTH） and 135 polybrominated xanthones（PBXTHs） in the standard state have been calculated at the B3LYP/6-31G＊ level using Gaussian 03 program.The isodesmic reactions were designed to calculate the standard enthalpy of formation（△fHθ） and standard free energy of formation（△fGθ） of PBXTH congeners.The relations of these thermodynamic parameters with the number and position of Br atom substitution（NPBS） were discussed,and it was found that there exist high correlation between thermodynamic parameters（entropy（Sθ）,△fHθ and △fGθ） and NPBS.According to the relative magnitude of their △fGθ,the relative stability order of PBXTH congeners was theoretically proposed.The relative rate constants of formation reactions of PBXTH congeners were calculated,Moreover,the values of molar heat capacity at constant pressure（Cp,m） from 200 to 1000 K for PBXTH congeners were also calculated,and the temperature dependence relation of them was obtained,suggesting very good relationships between Cp,m and temperature（T,T^1 and T^2） for almost all PBXTH congeners.

Relations Between Stabilities and Structures of Closo Borane Dianions

An effective method to investigate the stabilities of a series of new closo-BnHn2- （n = 12, 14, 16, 18, 20, 22, 24, 30） was put forward with the aid of G96PW91/SHC calculations. Stabilities are related to the relative stabilized energies （RSE） and the 2e3c bound geometries of closo-BnHn2-. The structures in which a boron atom connects to four atoms up to seven are stable and appear in many borides because of the lower relative stabilized energy. In geometries, both triangular and quadrangular faces are in favor of forming the structures of closo-BnHn2-. The energies of optimized geometries support the existence of these new compounds. By employing both RSE and AE per boron atom in cage, the stabilities were studied to predict the probabilities of unknown clusters in existence. The electron-deficient clusters can be understood that the positive holes should be disperse to every triangular face and lead to share the holes, wherever there are not enough electrons to occupy them. The negative charges which anions carry distribute to 2e3c bonds to increase the stabilities.

RELATIVE STABILITY FOR LOCAL MEDIAN ESTIMATE

Consider the nonparametric median regression model Y-ni = g(x(ni)) + epsilon(ni), 1 less than or equal to i less than or equal to n, where Y-ni's are the observations at the fixed design points x(ni) is an element of [0, 1], is an element of(ni)'s are independent identically distributed random variables with median zero, g(x) is the smooth function of interest, Suppose the local median estimate (g) over tilde(n, h)(x) of g(x) admits the Bahadur's representation. Under some regular conditions, the relative stability of the local median estimate is established in the L-2 sense.

RELATIVE CONFORMER STABILITY OF OPEN-CHAIN PHOSPHANE:A PM3 STUDY

The geometry and the energy of conformers of PnHn+2(n=2-9) have been studied with PM3 method. It is concluded that gauche interaction between adjacent lone electron pairs and gauche interaction between P-H bond with adjacent P-P bond are important for predicting the stable conformer of open-chain phosphoanes.

Study on the Characteristics of A New Hybrid Mooring System for DualPlatform Joint Operations

As the sustainable exploitation of marine resources develops,dual-platform joint operation has caught increasing attention.Dual-platform joint operation requires smaller relative motion between the two sub-platforms,which is normally difficult to be satisfied by the traditional mooring system.Therefore,a new hybrid mooring system is developed and studied in this article.To ensure safety during platform movements,both the number of anchor chains and the relative motion between the two sub-platforms are reduced in the new hybrid mooring system.By performing numerical simulations based on three-dimensional potential flow theory in AQWA and physical experiments,the performances of both the new hybrid and traditional mooring systems under two different wave conditions(i.e.,working wave and freak wave conditions) are systematically investigated.Regarding the new hybrid mooring system,the relative stability between the two sub-platforms of the new system is better,and the platforms can restore stability faster when affected by freak waves.

Thermodynamic Properties for Polybrominated Dibenzothiophenes by Density Functional Theory

The thermodynamic properties of 135 polybrominated dibenzothiophenes （PBDTs） in the gaseous state at 298.15 K and 1.013×10^5 Pa, are calculated using the density functional theory （the B3LYP/6-311G^＊＊） with Gaussian 03. Based on these data, the isodesmic reacflons are designed to calculate the standard enthalpy of formation （△fH^θ） and the standard Gibbs energy of formation （△fG^θ） of PBDTs. The relations of these thermodynamic parameters with the number and positionof bromine subsfituents （NPBS） are discussed, and it is found that there exist good correlations between othermody namic parameters （including heat capacity at constant volume, entropy, enthaipy, free energy, △fH^θ, △fG^θ） and NPBS. Thoe relative stability order of PBDT congeners is proposed theoretically based on the relative magnitude of their △fG^θ. In addition, the values of molar heat capacities at constant pressure （Cp,m） for PBDT c ongelaers are calculated.

Theoretical Studies on the Molecular Structures and Thermodynamic Properties of Polychlorinated Fluorenes

Geometric structures of 135 polychlorinated fluorene （PCFR） molecules were optimized using density functional theory （DFT） at the B3LYP/6-311G＊＊ level and their thermodynamic properties in the ideal gas state were calculated. The relations of these thermodynamic properties with the number and position of chlorine atoms were also explored, from which the relative stability of PCFR congeners was theoretically proposed according to the magnitude of the relative standard Gibbs free energy of formation （Δr,fGθ）. The results show that the geometric configuration of PCFR isomers is determined by the position of chlorine atoms. There exist two types of intramolecular weak interactions, i.e., C–H···Cl and Cl···Cl interactions in PCFR molecules. The change of ΔfHθ and ΔfGθ of most stable PCFR isomers with increasing the number of chlorine atoms is different from that in most unstable PCFR congeners. The values of ΔfHθ and ΔfGθ for PCFR isomers with the same number of chlorine atoms strongly depend on the position of chlorine atoms and the relative stability of PCFR congeners is mainly determined by intramolecular delocalized π bond and Cl···Cl nuclear repulsive interaction.

Comparative Study on Thermodynamic Properties and Stabilities of Polychloro-phenazines and Polychlorinated Dibenzo-p-dioxin

The thermodynamic properties and molecular volumes （Vm） of 76 polychlorophenazines （PCPZs） have been calculated at the B3LYP/6-31G^＊ level by using density functional theory. The isodesmic reactions were designed to calculate standard enthalpy of formation （△fH^θ） and standard free energy of formation （△fG^θ） of PCPZ congeners. According to the relative magnitude of their △fG^θ, the order of relative stability of PCPZ congeners was theoretically proposed. Comparing the results with those of polychlorinated dibenzo-p-dioxin （PCDD） isomers, it was found that S^θ, △fH^θ, △fG^θ, Vm and the order of relative stability of PCPZ congeners were quite similar to those of PCDDs.

Gas Phase Thermodynamic Properties of Polychlorinated Xanthones Predicted with DFT Method and Cl Substituted Position

The gas phase thermodynamic properties of 135 polychlorinated xanthones(PCXTs)are calculated using a combination of quantum mechanical computations performed with the Gaussian 03 program at the B3LYP/6-311G**level.It is found that the chlorine substitution pattern strongly influences the thermodynamic properties of the compounds.The thermodynamic properties of congeners with the same number of chlorines also depend on the chlorine substitution pattern,especially for ortho-substituted congeners.PCXT congeners with one phenyl ring fully chlorinated are found to be the least stable among the analogues.The effect of the chlorine substitution pattern is quantitatively studied by considering the number and position of Cl atom substitution(NPCS).The results show that the NPCS model may be used to predict the thermodynamic properties for all 135 PCXT congeners. In addition,the values of molar heat capacities at constant pressure(cp,m)from 200 to 1000 K for PCXT congeners are calculated,and the temperature dependence relation of this parameter is obtained using the least-squares method.

Theoretical Studies on the Molecular Structures and Thermodynamic Properties of Polychlorinated Acenaphthylenes

Geometric structures of 135 polychlorinated acenaphthylene （PCAC） molecules were optimized using density functional theory （DFT） at the B3LYP/6-311G^＊＊ level and some thermodynamic properties of them in the ideal gas state were calculated. The relations of these thermodynamic properties with the number and position of chlorine atoms were also explored, from which the relative stability of PCAC congeners was theoretically proposed according to the magnitude of the relative standard Gibbs free energy of formation （△r,fGθ）. The results show that all PCAC isomers have planar geometric configuration. There exists intramolecular Cl···Cl weak interaction in some PCAC molecules. The change of △fHθ and fGθ of most stable PCAC isomers with increasing the number of chlorine atoms is different from that in the least stable PCAC congeners. The values of fHθ and fGθ for PCAC isomers with the same number of chlorine atoms show a strong dependence on the position of chlorine atoms and the relative stability of PCAC congeners has close relation with the intramolecular Cl···Cl nuclear repulsive interaction.

Studies of Structural and Thermodynamic Properties for Polychlorinated Thianthrenes by Density Functional Theory

The structural and thermodynamic （PCTAs） in the ideal gas state at 298.15 K and 1.013 properties of 75 polychlorinated thianthrenes ×10^5 Pa have been calculated at the B3LYP/6- 31G＊ level using Gaussian 98 program. Based on the output data of Gaussian, the isodesmic reactions were designed to calculate standard enthalpy of formation （△fH^θ） and standard free energy of formation （△fH^θ） of PCTAs congeners. The relations of these thermodynamic parameters with the number and position of C1 atom substitution （Npcs） were discussed, and it was found that there exists high correlation between thermodynamic parameters （total energy （TE）, zero-point vibrational energy （ZPE）, thermal correction to energy （Eth）, heat capacity at constant volume （Cv^θ）, entropy （S^θ）, enthalpy （H^θ）, free energy （G^θ）, standard enthalpies of formation （△fH^θ） and standard Gibbs energies of formation （△fG^θ）） and Npcs. On the basis of the relative magnitude of their △fG^θ, the order of relative stability of PCTA congeners was theoretically proposed. In addition, the correlations between structural parameters and Npcs were also discussed. The good correlations were found between molecular average polarizability （α）, energy of the highest occupied molecular orbital （EHOMO）, molecular volume （Vm） and Npcs, and all R^2 values are larger than 0.95. Moreover, it was supposed that the isomer groups with higher toxicity should be Tri-CTA and TCTA.

Structural, electronic, and magnetic properties of boron cluster anions doped with aluminum:B_nAl^-(2 ≤ n ≤ 9)

The geometrical structures, relative stabilities, electronic and magnetic properties of small BnAl-（2〈n〈9）clusters are systematicalyy investigated by using the first-principles density functional theory. The results show that the A1 atom prefers to reside either on the outer-side or above the surface, but not in the centre of the clusters in all of the most stable BnAl-（2〈n〈9） isomers and the one excess electron is strong enough to modify the geometries of some specific sizes of the neutral clusters. All the results of the analysis for the fragmentation energies, the second-order difference of energies, and the highest occupied-lowest unoccupied molecular orbital energy gaps show that B4A1- and B8A1- clusters each have a higher relative stability. Especially, the BsA1-cluster has the most enhanced chemical stability. Furthermore, both the local magnetic moments and the total magnetic moments display a pronounced oddeven oscillation with the number of boron atoms, and the magnetic effects arise mainly from the boron atoms except for the B7A1- and BgA1- clusters.

Theoretical Studies on the Molecular Structures and Thermodynamic Properties of Polychlorinated Fluoranthenes

DFT-B3LYP/6-311G＊＊ method has been used to optimize molecular geometric structures of 527 polychlorinated fluoranthene（PCFRT） congeners and calculate their thermo-dynamic properties in the ideal gas state,such as heat capacity at constant volume（Cv）,entropy（S）,standard enthalpy of formation（ΔfH） and standard Gibbs free energy of formation（ΔfG）.The relations of Cv,S,ΔfH and ΔfG with the number and position of chlorine atoms have also been explored,from which the relative stability of PCFRT congeners was theoretically proposed according to the magnitude of the relative standard Gibbs free energy of formation（Δr,fG）.It was found that some of the PCFRT isomers are in a nonplanar configuration and there are intramolecular Cl…Cl weak interactions in some of the isomers.With increasing the number of chlorine atoms,the values of ΔfH and ΔfG of the most stable PCFRT isomers decrease initially and then increase.The values of ΔfH and ΔfG of PCFRT congeners with the same number of chlorine atoms show a strong dependence on the positions of chlorine atoms.The relative thermodynamic stability of PCFRT isomers is determined mainly by intramolecular adjacent Cl…Cl nuclear repulsive interaction between Cl atoms at two different six-membered rings.Most PCFRT congeners are easier to form thermodynamically than their parent compound.

A density functional theory structures, stabilities, and study on size-dependent electronic properties of bimetallic MnAgm （M=Na, Li; n ＋ m ≤ 7） clusters

The equilibrium geometries, relative stabilities, and electronic properties of MnAgm（M=Na, Li; n ＋ m ≤ 7） as well as pure Agn, Nan, Lin （n ≤ 7） clusters are systematically investigated by means of the density functional theory. The optimized geometries reveal that for 2 ≤ n ≤ 7, there are significant similarities in geometry among pure Agn, Nan, and Lin clusters, and the transitions from planar to three-dimensional configurations occur at n = 7, 7, and 6, respectively. In contrast, the first three-dimensional （3D） structures are observed at n ＋ m = 5 for both NanAgm and LinAgm clusters. When n ＋ m ≥5, a striking feature is that the trigonal bipyramid becomes the main subunit of LinAgm. Furthermore, dramatic odd-even alternative behaviours are obtained in the fragmentation energies, secondorder difference energies, highest occupied and lowest unoccupied molecular orbital energy gaps, and chemical hardness for both pure and doped clusters. The analytic results exhibit that clusters with an even electronic configuration （2, 4, 6） possess the weakest chemical reactivity and more enhanced stability.

DFT Study on the Thermodynamic Properties of Poly-bromine Carbazole

The molecular structures of 135 poly-bromine carbazole （PBCZs） compounds were fully optimized at the B3LYP/6-31G＊ level, and their thermodynamic properties at 98.15 K, 1.013 ×105 Pa were consequently obtained. Based on our isodesmic reaction, standard formation heat （ΔfHθ） and standard formation free energy （ΔfGθ） of PBCZs were calculated. Furthermore, the relationship between thermodynamic parameters and the position and number （NPBS） of Brsubstitution were also discussed. To our interest, a good dependence can be observed among entro- py （Sθ）, ΔfHθ, ΔfGθ and NPBS. Ultimately, the theoretical stability order of isomers can be decided judging from the ΔfGθ value.

A density functional theory study on size-dependent structures,stabilities,and electronic properties of bimetallic M_nAg_m(M=Na,Li;n + m≤7) clusters

The equilibrium geometries,relative stabilities,and electronic properties of Mn Agm(M=Na,Li;n + m ≤ 7) as well as pure Ag n,Na n,Li n(n ≤ 7) clusters are systematically investigated by means of the density functional theory.The optimized geometries reveal that for 2 ≤ n ≤ 7,there are significant similarities in geometry among pure Ag n,Na n,and Li n clusters,and the transitions from planar to three-dimensional configurations occur at n = 7,7,and 6,respectively.In contrast,the first three-dimensional(3D) structures are observed at n + m = 5 for both Na n Ag m and Li n Ag m clusters.When n + m ≥ 5,a striking feature is that the trigonal bipyramid becomes the main subunit of Li n Ag m.Furthermore,dramatic odd-even alternative behaviours are obtained in the fragmentation energies,secondorder difference energies,highest occupied and lowest unoccupied molecular orbital energy gaps,and chemical hardness for both pure and doped clusters.The analytic results exhibit that clusters with an even electronic configuration(2,4,6) possess the weakest chemical reactivity and more enhanced stability.

Relative Stability of Boiling of FC-72 and HFE-7100 with Applications toElectronic Device Cooling

This paper investigates the relative stability between nucleate and film boiling modes of FC-72 and HFE-7100, which have potential to electronic device cooling applications. Equilibrium heat flux, qc, which refers to as an index for measuring the relative stability of boiling, was obtained at a liquid subcooling of 0-20 K. Experimental results reveal that (1) qc increases with liquid subcooling; (2) although the FC-72 exhibits a higher critical heat flux (CHF) than does the HFE-7100, somewhat unexpectedly, the equilibrium heat flux for the latter is greater than the former. Restated, at a prescribed heat flux, the risk to burnout for boiling of FC-72 is higher than that of HFE-7100. The shift in boiling curves interprets the experimental findings.

CONFLICT ANALYSIS APPROACHES FOR INVESTIGATING ATTITUDES AND MISPERCEPTIONS IN THE WAR OF 1812

Formal systems engineering approaches to modeling misperceptions and attitudes are employed within the framework of the graph model for conflict resolution to systematically study the War of 1812 between the United States of America and Great Britain in order to provide enhanced insights into the causes of the war. More specifically, relational definitions for preferences, movements and stability concepts are defined for describing the attitudes and associated behavior of decision makers involved in a conflict. To capture misperceptions of decision makers in the War of 1812, attitudes are studied within the structure of a hypergame. Combining attitudes and misperceptions within the paradigm of the graph model furnishes the flexible analytical tool which demonstrates that misunderstanding of attitudes by Great Britain and the United States may have contributed to the outbreak of this nasty war.

Weak Finite Determinacy of Relative Map-Germs

The weak finite determinacy of relative map-germs is studied. The authors first give the concept of weak finite determination, and then give several sufficient conditions for a relative map-germ to be weak finitely determined, which is an important complement to Mather＇s work. Moreover, us an application, it is proven that the relative stable map-germs are weak finitely determined.