Calculated density

The Lee and Kesler method for calculating densities is given in article 4.3.1.1 its average accuracy is about 1%, when the pressure is less than 100 bar. 

To find appropriate empirical pair potentials from the known protein structures in the Brookhaven Protein Data Bank, it is necessary to calculate densities for the distance distribution of Ga-atoms at given bond distance d and given residue assignments ai,a2- Up to a constant factor that is immaterial for subsequent structure determination by global optimization, the potentials then ciiiergo as the negative logarithm of the densities. Since... 

Anhydrous magnesium nitrate [10377-60-3] Mg(N02)2, is very difficult to isolate. The commercial product is the deUquescent hexahydrate [13446-18-9] Mg(N02)2 6H20. As illustrated in the solubiUty curve in Figure 7, the hexahydrate is the stable soHd phase between —18 and 55—56°C. Properties are given in Table 17 (1 4). The unit ceU contains two formula units and the calculated density is 1.643 g/cm. ... 

Density. Although the polymer unit cell dimensions imply a calculated density of 1.33 g/cm at 20°C, and extrapolation of melt density data indicates a density of 1.13 g/cm at 20°C for the amorphous phase, the density actually measured is 1.15—1.26 g/cm, which indicates the presence of numerous voids in the stmcture. 

The value for the heat of fusion of PPS, extrapolated to a hypothetical 100% crystalline state, is not agreed upon in the literature. Reported values range from approximately 80 J/g (19 cal/g) (36,96,101) to 146 J/g (35 cal/g) (102), with one intermediate value of 105 J/g (25 cal/g) (20). The lower value, 80 J/g, was originally measured by thermal analysis and then correlated with a measure of crystallinity deterrnined by x-ray diffraction (36). The value of 146 J/g was deterrnined independendy on uniaxiaHy oriented PPS film samples by thermal analysis, density measurement via density-gradient column, and the use of a calculated density for 100% crystalline PPS to arrive at a heat of fusion for 100% crystalline PPS (102). The value of 105 J/g was obtained by measuring the heats of fusion of weU-characterized linear oligomers of PPS and extrapolation to infinite molecular weight. 

Crystal Structure. The crystal stmcture of PVDC is fairly well estabhshed. Several unit cells have been proposed (63). The unit cell contains four monomer units with two monomer units per repeat distance. The calculated density, 1.96 g/cm, is higher than the experimental values, which are 1.80—1.94 g/cm at 25°C, depending on the sample. This is usually the case with crystalline polymers because samples of 100% crystallinity usually cannot be obtained. A dkect calculation of the polymer density from volume changes during polymerization yields a value of 1.97 g/cm (64). If this value is correct, the unit cell densities may be low. 

Crystal Structure. Diamonds prepared by the direct conversion of well-crystallized graphite, at pressures of about 13 GPa (130 kbar), show certain unusual reflections in the x-ray diffraction patterns (25). They could be explained by assuming a hexagonal diamond stmcture (related to wurtzite) with a = 0.252 and c = 0.412 nm, space group P63 /mmc — Dgj with four atoms per unit cell. The calculated density would be 3.51 g/cm, the same as for ordinary cubic diamond, and the distances between nearest neighbor carbon atoms would be the same in both hexagonal and cubic diamond, 0.154 nm. 

J Li, L Noodleman, DA Case. Electronic structure calculations Density functional methods with applications to transition metal complexes. In EIS Lever, ABP Lever, eds. Inorganic Electronic Structure and Spectroscopy, Vol. 1. Methodology. New York Wiley, 1999, pp 661-724. 

The existence of carbon nanotubes with diameters small compared to the de Broglie wavelength has been described by Iijima[l,2,3] and others[4,5]. The energy band structures for carbon nanotubes have been calculated by a number of authors and the results are summarized in this issue by M.S. Dresselhaus, G. Dres-selhaus, and R. Saito. In short, the tubules can be either metallic or semiconducting, depending on the tubule diameter and chirality[6,7,8]. The calculated density of states[8] shows singularities... 

Fig. 4. Calculated density of states for two zigzag individual SWCNTs with (a) semiconducting (10, 0) and (b) metallic (9, 0) configurations. Tight-binding approximation was used for the calculation [6].

The calculated density functional KS-LCAO energy is denoted E(RB-LYP). 

Reality Check In FCC unit cells, the fraction of empty space is 0.26. When this is factored into the above, the calculated density of silver becomes 14.3 — (0.26)(14.3) =... 

Attempts to brominate benzothiazoles with bromine in acetic acid at room temperature have given only perbromides, but when these were heated in ethanolic solution, products in which bromine had substituted in the benzene moiety were detected. At 100°C bromine in acetic acid gave rise to the 4,6-dibromo derivative in accord with calculated -densities (70BSF2705). Vapor-phase bromination gave the 2-bromo product (84MI27). 

All of the observed reflections could be indexed on the basis of a cubic unit cell with Oo = 11.82 A the estimated probable error is 0.01 A. The only systematic absences were hhl with l odd this is characteristic of the space group 0 -PmP>n, which also was reported by von Stackelberg from his single-crystal work on sulfur dioxide hydrate. For 46 H20 and 6 Cl2 in the unit cell the calculated density is 1.26 densities reported by various observers range from 1.23 to 1.29. 

Li, J., Noodleman, L., Case, D.A. Electronic stmcture calculations Density functional methods with applications to transition metal complexes. In Solomon, E.I., Lever, A.B.P. (eds.) Inorganic Electronic Stmcture and Spectroscopy, vol. 1, P- 661. Wiley, New York (1999)... 

A selected subset of the reported densities is fit to functions of temperature using the least squares criterion. Up to a boundary temperature Tb (approximately 0.87 c), the calculated density px is represented by a polynomial in temperature with coefficients ak of order p,... 

Step 13. Generate the output table of temperature, observed densities, estimated uncertainties, and difference between observed and calculated densities and arrange it in order of year of publication with authors. For data from a particular source, arrange in order of temperature. 

Testing a Set of Deviations between Observed and Calculated Density Values for a Random Distribution... 

Table 17. DMSO-distances, some close contact data, and calculated densities in the DMSO-inelusions of /, 20, 26, and 41 (cf. Fig. 24)...

This host network, termed the helical tubuland structure type 7,8), is unique. The walls of the canals are lined only by aliphatic hydrocarbon, and the hydrogen bonded spines are insulated from the guest canals. Powder diffraction and IR measurements indicate that when 1 is crystallised from acetonitrile the same host crystal structure occurs, but devoid of guest. This has the unusually low calculated density, 1.02 g cm 3. 

Figure 4.12 Left experimental line profile for Ti02(l 1 0) along [1 1 0] in the presence of pristine defects (Ovac, OHbr) and undissociated water molecule for V= 1.5 V, / = 0.08 nA (80 K). Right calculated density contour (top, 1.5 V,...

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