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The density matrix is a representation of a linear operator called the density operator. The density matrix is obtained from the density operator by a choice of an orthonormal basis in the underlying space. [2] In practice, the terms density matrix and density operator are often used interchangeably.
Python-based Simulations of Chemistry Framework (PySCF) is an ab initio computational chemistry program natively implemented in Python program language. [ 1 ] [ 2 ] The package aims to provide a simple, light-weight and efficient platform for quantum chemistry code developing and calculation.
Mulliken charges arise from the Mulliken population analysis [1] [2] and provide a means of estimating partial atomic charges from calculations carried out by the methods of computational chemistry, particularly those based on the linear combination of atomic orbitals molecular orbital method, and are routinely used as variables in linear regression (QSAR [3]) procedures. [4]
A graphical intuition of purity may be gained by looking at the relation between the density matrix and the Bloch sphere, = (+), where is the vector representing the quantum state (on or inside the sphere), and = (,,) is the vector of the Pauli matrices.
The fidelity between two quantum states and , expressed as density matrices, is commonly defined as: [1] [2] (,) = ().The square roots in this expression are well-defined because both and are positive semidefinite matrices, and the square root of a positive semidefinite matrix is defined via the spectral theorem.
They may also include density functional theory (DFT), molecular mechanics or semi-empirical quantum chemistry methods. The programs include both open source and commercial software. Most of them are large, often containing several separate programs, and have been developed over many years.
In quantum chemistry, n-electron valence state perturbation theory (NEVPT) is a perturbative treatment applicable to multireference CASCI-type wavefunctions.It can be considered as a generalization of the well-known second-order Møller–Plesset perturbation theory to multireference complete active space cases.
Density matrix can be, for example, / in a finite-dimensional system, or a thermal state in infinite dimensional systems. Generalization and relations to Bures metric and quantum fidelity [ edit ]