Recall that PCM electrostatics calculations require the solution of the set of linear equations given in Eq. (11.2), to determine the vector of apparent surface charges. The precise forms of the matrices and depend upon the particular PCM (Table 11.3), but in any case they have dimension , where is the number of Lebedev grid points used to discretize the cavity surface. Construction of the matrix affords a numerically exact solution to Eq. (11.2), whose cost scales as in CPU time and in memory. This cost is exacerbated by smooth PCMs, which discard fewer interior grid points so that tends to be larger, for a given solute, as compared to traditional discretization schemes. For QM solutes, the cost of inverting is usually negligible relative to the cost of the electronic structure calculation, but for the large values of that are encountered in MM/PCM or QM/MM/PCM jobs, the cost of inverting is often prohibitively expensive.
To avoid this bottleneck, Lange and Herbert376 have developed an iterative conjugate gradient (CG) solver for Eq. (11.2) whose cost scales as in CPU time and in memory. A number of other cost-saving options are available, including efficient pre-conditioners and matrix factorizations that speed up convergence of the CG iterations, and a fast multipole algorithm for computing the electrostatic interactions.579 Together, these features lend themselves to a solution of Eq. (11.2) whose cost scales as in both memory and CPU time, for sufficiently large systems.376 Currently, these options are available only for C-PCM, not for SS(V)PE/IEF-PCM.
Listed below are job control variables for the CG solver, which should be specified within the $pcm input section. Researchers who use this feature are asked to cite the original SWIG PCM references532, 533 as well as the reference for the CG solver.376
A sample input file for the linear-scaling QM/MM/PCM methodology can be found in the $QC/samples directory, under the name QMMMPCM_crambin.in. This sample involves a QM/MM description of a protein (crambin) in which a single tyrosine side chain is taken to be the QM region. The entire protein is immersed in a dielectric using C-PCM with SWIG discretization.