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Density is a measure of how much mass is contained in a given volume. It is typically expressed in grams per cubic centimeter or kilograms per liter. Higher den...
Density is a measure of how much mass is contained in a given volume. It is typically expressed in grams per cubic centimeter or kilograms per liter. Higher density indicates that a substance has a larger amount of mass packed into a smaller volume, while lower density indicates that a substance has a smaller amount of mass in a larger volume.
Trong vật lý, mật độ là một đại lượng quan trọng để mô tả tính chất vật lý của các vật liệu và có thể được tính toán bằng cách chia khối lượng của vật liệu cho thể tích của nó. Mật độ cũng có thể thay đổi theo nhiệt độ và áp suất. Ví dụ, nước có mật độ là 1 gram trên mỗi centimet vuông ở nhiệt độ phổ biến, nhưng mật độ sẽ thay đổi với nhiệt độ và áp suất khác nhau. Mật độ cũng được sử dụng để xác định tính chất của vật liệu, như sự nổi hay chìm của chúng trong nước.
Mật độ cũng có thể được sử dụng để phân loại các vật liệu và hỗ trợ trong việc xác định thành phần và tính chất của chúng. Ví dụ, trong ngành công nghiệp và kỹ thuật, mật độ được sử dụng để kiểm tra chất lượng của các hợp chất và vật liệu, đặc biệt là khi xác định tính chất của kim loại và hợp kim.
Trong lĩnh vực khoa học đất đai, mật độ đất cũng là một đặc tính quan trọng và được sử dụng để đánh giá cấu trúc và hàm lượng của đất. Nó có vai trò quan trọng trong việc xác định khả năng tiếp xúc giữa đất và nước, cũng như ảnh hưởng đến sự phát triển của hệ thống cỏ và cây trồng.
Density-functional thermochemistry. III. The role of exact exchange Journal of Chemical Physics - Tập 98 Số 7 - Trang 5648-5652 - 1993
Despite the remarkable thermochemical accuracy of Kohn–Sham density-functional theories with gradient corrections for exchange-correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact-exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange-correlation functional containing local-spin-density, gradient, and exact-exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first- and second-row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.
A consistent and accurate<i>ab initio</i>parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu Journal of Chemical Physics - Tập 132 Số 15 - 2010
The method of dispersion correction as an add-on to standard Kohn–Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination numbers (CN). They are used to interpolate between dispersion coefficients of atoms in different chemical environments. The method only requires adjustment of two global parameters for each density functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of atomic forces. Three-body nonadditivity terms are considered. The method has been assessed on standard benchmark sets for inter- and intramolecular noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean absolute deviations for the S22 benchmark set of noncovalent interactions for 11 standard density functionals decrease by 15%–40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coefficients also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.
Estimation of the Concentration of Low-Density Lipoprotein Cholesterol in Plasma, Without Use of the Preparative Ultracentrifuge Clinical Chemistry - Tập 18 Số 6 - Trang 499-502 - 1972
Abstract
A method for estimating the cholesterol content of the serum low-density lipoprotein fraction (Sf0-20) is presented. The method involves measurements of fasting plasma total cholesterol, triglyceride, and high-density lipoprotein cholesterol concentrations, none of which requires the use of the preparative ultracentrifuge. Comparison of this suggested procedure with the more direct procedure, in which the ultracentrifuge is used, yielded correlation coefficients of .94 to .99, depending on the patient population compared.
Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction Journal of Computational Chemistry - Tập 27 Số 15 - Trang 1787-1799 - 2006
AbstractA new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97‐D is proposed. It is based on Becke's power‐series ansatz from 1997 and is explicitly parameterized by including damped atom‐pairwise dispersion corrections of the form C6 · R−6. A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross‐validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97‐D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol−1. The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C6 · R−6 terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97‐D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance. © 2006 Wiley Periodicals, Inc. J Comput Chem 2006
Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis Canadian Journal of Physics - Tập 58 Số 8 - Trang 1200-1211 - 1980
We assess various approximate forms for the correlation energy per particle of the spin-polarized homogeneous electron gas that have frequently been used in applications of the local spin density approximation to the exchange-correlation energy functional. By accurately recalculating the RPA correlation energy as a function of electron density and spin polarization we demonstrate the inadequacies of the usual approximation for interpolating between the para- and ferro-magnetic states and present an accurate new interpolation formula. A Padé approximant technique is used to accurately interpolate the recent Monte Carlo results (para and ferro) of Ceperley and Alder into the important range of densities for atoms, molecules, and metals. These results can be combined with the RPA spin-dependence so as to produce a correlation energy for a spin-polarized homogeneous electron gas with an estimated maximum error of 1 mRy and thus should reliably determine the magnitude of non-local corrections to the local spin density approximation in real systems.