According to DigoPaul, correlation is called the reciprocal or corresponding link that exists between two or more elements. The concept is used in different ways according to the context.
In the field of mathematics and statistics, correlation refers to proportionality and the linear relationship that exists between different variables. If the values of one variable change systematically with respect to the values of another, the two variables are said to be correlated.
Correlation is the linear relationship and the proportionality that is recorded between various variables.
Suppose we have a variable R and a variable S. As the values of R increase, the values of S increase. Similarly, as the values of S increase, the values of R increase. Therefore there is a correlation between the variables R and S.
We can present this same example graphically if we think about the accounting of a company, specifically in two variables that record “the expenses for purchasing products” and the “total stock in the warehouse”; it is correct to say that as the first increases so does the second, and that it is not possible to avoid this correlation.
Dependency between variables
It can be noted that the correlation is the measure that is recorded of the dependence between different variables. The degree of correlation can be measured by so-called correlation coefficients, such as the intraclass correlation coefficient, the Spearman correlation coefficient, and the Jaspen coefficient.
It is important to note that the existence of a statistical correlation between two events does not imply that there is a causal connection between them. This fallacious belief is summarized with the Latin expression Cum hoc ergo propter hoc, which is usually summarized as “correlation does not imply causality”. The presumed causality in the correlation may be due to coincidence or the existence of some unknown factor, for example.
Electronic correlation refers to the interaction of electrons in a quantum system.
The electronic correlation
The idea of electronic correlation, on the other hand, alludes to the interaction that electrons maintain in a quantum-type system. This concept falls within the field of quantum mechanics, a discipline that physics uses to fundamentally describe nature, taking small spatial scales as a reference.
Physics borrowed this term from statistics, where it is used to define the case where two distribution functions are not independent of each other. We understand by distribution function that which serves to describe the probability that the variable to which it is associated is less than or equal to another, around which it is applied.
Let us think, for example, of two electrons, a and b ; If we defined the distribution function p(ra,rb) to establish the joint probability that the first is found in ra and the second in rb, we would be talking about a correlation between them as long as it was not equal to the product of p(ra) by p(rb), that is, of the individual probabilities of each variable.
The case for quantum chemistry
Quantum chemistry, on the other hand, is a branch of chemistry that can be applied to quantum field theory and quantum mechanics; it is about the description by mathematical means of the fundamental behavior of matter, on a scale that is measured in molecules. In the so-called Hartree–Fock method, an approximation of the quantum mechanical equations for elementary particles called fermions, there is an asymmetric wave function describing a group of electrons that is only approximated by a particular technique, known as the Slater determinant..
On the other hand, exact wavefunctions cannot always be represented as unique determinants, since this leaves out the correlation between electrons whose spins are opposite (spin is a property of elementary particles that describes an intrinsic angular momentum whose value does not change).