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Exhibit 1: Ground state hyperfine splitting of the H atom: 1420405751767(1) mHz (present most accurate experiment) 142045199 mHz (present most accurate theory) The error in the theory is due to the difficulty in treating the nuclear structure (2 up quarks + 1 down). Exhibit 2: Ground state hyperfine splitting of the muonium atom: 4463302780(050) Hz (...


15

FCI doesn't really have "occupied orbitals" in the mean-field sense, since all orbitals become fractionally occupied. What one usually does is look at natural orbitals, which one gets by diagonalizing the one-particle density matrix; then each spin-orbital has some occupation number $f_n \in [0,1]$. However, DFT isn't really aiming to reproduce the ...


9

The Davidson-Method is the best algorithm when you want a comparatively small number of eigenvectors/eigenvalues from a sparse, diagonally dominant matrix. MKL doesn’t have a sparse matrix diagonalization method, but it’s a good idea to use it for the Linear Algebra operations used when implementing Davidson. If you want ALL the eigenvectors then you ...


9

Following Nike Dattani's suggestion, I now add some comparisons of the Davidson method with methods that are more "modern" than it, to supplement the existing answers which compared the Davidson method with methods that predates it. However my answer will be more or less off-topic because I will mainly talk about disadvantages of the Davidson ...


9

Let's go back to the original paper where the fcidump format was first proposed: A determinant based full configuration interaction program by Peter Knowles (lead author of the MOLPRO program, along with Hans-Joachim Werner) and Nick Handy in 1989. This algorithm is still used by a lot of people today, and is considered one of the most efficient ways to do ...


7

MS2 is related to the spin. Specifically, it is the number of unpaired electrons. Your molecule is a singlet, which is why it says 0. ORBSYM is the list of symmetries for each orbital. In this case $\ce{H2}$ is in $D_{\infty h}$ but almost all electronic structure codes do not support non-Abelian groups, so instead we would almost always use $D_{2h}$. The ...


7

To supplement Cody's excellent answer, Davidson diagonalization originates from quantum chemistry, where solving configuration interaction problems requires diagonalizing the Hamiltonian in the space of electron configurations. The Davidson algorithm and refinements thereof enabled full configuration interaction calculations with matrix sizes of $10^9 \times ...


6

GAMESS also should be able to calculate analytic hessian for the full CI case. From the GAMESS manual: $FORCE group (optional, relevant for RUNTYP=HESSIAN,OPTIMIZE,SADPOINT) This group controls the computation of the hessian matrix (the energy second derivative tensor, also known as the force constant matrix), and an optional harmonic vibrational analysis....


6

Analytical Hessians have been derived for pretty much everything; they just aren't available in most programs. CFOUR has analytical vibrational frequencies i.e. nuclear Hessians for HF and the following post-HF methods: MP2, MP3, MP4, CC2, CCD, QCISD, CCSD, QCISD(T), CCSD(T), CCSDT-n (n=1-4), CC3, CCSDT. Kállay's MRCC program has analytical Hessians for ...


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