Introduction to Density

Matter can be defined as something that has mass and occupies space. If something occupies space, it has volume. Therefore, matter may be defined as any substance that has density. As an intrinsic physical property of matter, density can be used to help identify and differentiate substances. The method that is used to determine the density depends on the substance being measured. Is it a solid, liquid, or gas If it is a solid, is it regularly shaped Is it porous What level of precision is required  

In the laboratory density is one of the most important characteristics that we have to describe various substances. It is also one of the most important tasks that a chemical technician performs. For example, to confirm the identity of an incoming raw material one of the tests technicians may perform is density. Is it sodium chloride or magnesium sulfate or sucrose  

In the design of parts for a particular device, density can be an important factor in the selection of a material, especially when deciding whether to use metal or plastic. For example, some specially designed plastics may cost 5/lb compared to l/lb for a steel part. If the plastic has a density of 0.04 lb/in.3 and the steel has a density of 0.28 lb/in., the difference in price will be small if the part has a small volume. Using the figures above, the cost of 1 in. would be 0.20 for the plastic part and 0.28 for the steel part. 

The density of a substance may be obtained simply by measuring its mass and volume and making the necessary calculation. The units for mass are typically given in grams, while the units for volume may be milhhters (cubic centimeters) or liters, depending on the physical state of the substance. The volume of solids and liquids is given in cubic centimeters or milliliters. 

The volume of a substance changes with the temperature, thus affecting its density. When determining the density of a substance, the temperature should also be measured and recorded. It is generally reported along with the density value in one of the following formats  

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Libero J. Bartolotti and Ken Flurchick, An Introduction to Density Functional Theory. 

Bartolotti LJ, Flurchick K. An introduction to density functional theory. In Lipkowitz KB, Boyd DB, eds. Reviews in Computational Chemistry. Vol. 7. New York VCH, 1995 187-216. 

We are particularly grateful to Eric Short for a critical reading of Chapters 2 and 3, for the additional calculations contained in Chapters 5 and 10, and for the brief introduction to Density Functional Theory, which is inserted as an Appendix to Chapter 5. 

J. M. Seminario, An Introduction to Density Functional Theory in Chemistry, in Modem Density Functional Theory a Tool for Chemistry, edited by J. M. Seminario and P. Politzer (Elsevier Science, Amsterdam, 1995). 

A comprehensive overview of quantum mechanics is given by Cohen-Tannoudji et al. (1977), and another good book is by Levine (2000). A staple text on solid-state physics is by Ashcroft and Mermin (1976). A thorough introduction to density-functional theory is given by Parr and Yang (1989). Two good books to learn more about molecular dynamics simulations are by Allen and Tildesley (1987) and Frenkel and Smit (1996). To learn more about pseudopotential methods, two sources with which to begin are by Pickett (1989) and Bachelet et al. (1982). 

We also present a brief introduction to density functional theory (DFT). This is a newer method that is steadily gaining popularity. We do not develop DFT as extensively as conventional ab initio theory, in part because the latter is the rigorous implementation of our qualitative notions of structure and bonding. So, while DFT may in time become the computational method of choice, ab initio molecular orbital theory is a pedagogically more useful introduction to advanced molecular quantum mechanics. 

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