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Based on my understanding, an ORB file contains the atomic orbital coefficients corresponding to each molecular orbital. That is if Ψ is my molecular orbital and φ_i is the i-th atomic orbital then
Ψ = Σ_i c_i * φ_i. Given a basis set how does the program calculate the coefficients c_i? Is it using least squares linear regression? Is it a constrained optimization problem meaning we impose constraints on the coefficients? Given a molecular orbital which has only real values how does the program deal with basis functions that have imaginary parts such as p orbitals with m=+-1?
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