17. Why do I get out of memory errors with HyperNMR?

The memory requirements for the calculation of a spectrum with HyperNMR come from three sources that depend on the number of nuclear spin states. The number of spin states that must be considered (let me call this N) can be up to 2^M (less if there are equivalent atoms defined) where M is the number of NMR atoms.

Each spin state requires (in bytes):

4 * [(# of non-equivalent NMR atoms) + (# of possible total spin) + 2]

Another large memory requirement is for three double precision square matrices (for a Hamiltonian, spin S eigenvectors and spin S+1 eigenvectors). The dimension of each is up to (depending on equivalancies) the largest binomial coefficient for N, namely N!/[i!(N-i)!] where i is the integer closest to N/2. The time required to calculate the spectrum is dominated by the diagonalizations of the N+1 Hamiltonian matrices (with dimensions given by the binomial coefficients for N).

The third large memory requirement is 20 bytes per transition, for storing energy, intensity and degeneracy. The number of transitions may be as large as the sum of the pairwise products of neighbouring binomial coefficients for N, depending on equivalencies.

For most PCs (i.e. 8-16 Mb), spectra for 12 non-equivalent NMR atoms are practical, with some use of virtual memory. You can go somewhat higher if you have equivalent atoms. You can also consider larger systems by reducing the set of NMR atoms. In comparison, similar programs from QCPE are limited to 8 nuclei.

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