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Canonical stress–energy tensor, a conserved current associated with translations through space and time; Canonical theory, a unified molecular theory of physics, chemistry, and biology; Canonical conjugate variables, pairs of variables mathematically defined in such a way that they become Fourier transform duals
Contributing structures of the carbonate ion. In chemistry, resonance, also called mesomerism, is a way of describing bonding in certain molecules or polyatomic ions by the combination of several contributing structures (or forms, [1] also variously known as resonance structures or canonical structures) into a resonance hybrid (or hybrid structure) in valence bond theory.
Various algorithms for generating canonical SMILES have been developed and include those by Daylight Chemical Information Systems, OpenEye Scientific Software, MEDIT, Chemical Computing Group, MolSoft LLC, and the Chemistry Development Kit. A common application of canonical SMILES is indexing and ensuring uniqueness of molecules in a database.
The canonical ensemble is the only ensemble with constant N, V, and T that reproduces the fundamental thermodynamic relation. [9] Statistical equilibrium (steady state): A canonical ensemble does not evolve over time, despite the fact that the underlying system is in constant motion. This is because the ensemble is only a function of a ...
Localized molecular orbitals (LMO) [4] are obtained by unitary transformation upon a set of canonical molecular orbitals (CMO). The transformation usually involves the optimization (either minimization or maximization) of the expectation value of a specific operator.
We identify canonical coordinates (such as x in the example above, or a field Φ(x) in the case of quantum field theory) and canonical momenta π x (in the example above it is p, or more generally, some functions involving the derivatives of the canonical coordinates with respect to time): = (/).
Constructing a density matrix using a canonical ensemble gives a result of the form = / (), where is the inverse temperature () and is the system's Hamiltonian. The normalization condition that the trace of ρ {\displaystyle \rho } be equal to 1 defines the partition function to be Z ( β ) = t r exp ( − β H ) {\displaystyle Z(\beta ...
The grand canonical ensemble is the only ensemble with constant , V, and T that reproduces the fundamental thermodynamic relation. [5] Statistical equilibrium (steady state): A grand canonical ensemble does not evolve over time, despite the fact that the underlying system is in constant motion. Indeed, the ensemble is only a function of the ...