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In quantum chemistry, the quantum theory of atoms in molecules (QTAIM), sometimes referred to as atoms in molecules (AIM), is a model of molecular and condensed matter electronic systems (such as crystals) in which the principal objects of molecular structure - atoms and bonds - are natural expressions of a system's observable electron density distribution function.
An atomic formula or atom is simply a predicate applied to a tuple of terms; that is, an atomic formula is a formula of the form P (t 1,…, t n) for P a predicate, and the t n terms. All other well-formed formulae are obtained by composing atoms with logical connectives and quantifiers. For example, the formula ∀x. P (x) ∧ ∃y. Q (y, f (x ...
Each carbon atom contributes one electron to a delocalized system of electrons that is also a part of the chemical bonding. The delocalized electrons are free to move throughout the plane. For this reason, graphite conducts electricity along the planes of carbon atoms, but does not conduct in a direction at right angles to the plane.
The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject.
Alternately, the atomic mass of a carbon-12 atom may be expressed in any other mass units: for example, the atomic mass of a carbon-12 atom is 1.992 646 882 70 (62) × 10 −26 kg. As is the case for the related atomic mass when expressed in daltons , the relative isotopic mass numbers of nuclides other than carbon-12 are not whole numbers, but ...
In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy.Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system's total energy.
Arithmetic is the fundamental branch of mathematics that studies numbers and their operations. In particular, it deals with numerical calculations using the arithmetic operations of addition, subtraction, multiplication, and division. [1]
The rationale of crystal geometry to atom solubility prediction is summarized in the Hume-Rothery rules and Pauling's rules. Substitutional solid solution strengthening occurs when the solute atom is large enough that it can replace solvent atoms in their lattice positions. Some alloying elements are only soluble in small amounts, whereas some ...