Low-order tensor approximations for electronic wave functions: Hartree-Fock method with guaranteed precision

Here we report a formulation of the Hartree-Fock method in an adaptive multiresolution basis set of spectral element type. A key feature of our approach is the use of low-order tensor approximations for operators and wave functions to reduce the steep rise of storage and computational costs with the number of degrees of freedom that plague finite element computations. As a proof of principle we implemented Hartree-Fock method without explicit storage of the full-dimensional wave function and with guaranteed precision (microhartree precision for up to 14 electron systems is demonstrated). Even for the one-electron method the use of low-order tensor approximation reduces storage relative to the full representation, albeit with modest increase in cost. Preliminary tests for explicitly-correlated two-electron (six-dimensional) wave function suggest a factor of 50 savings in storage. At least correlated two-electron methods should be feasible with our approach on modern workstations with guaranteed precision. (C) 2011 American Institute of Physics. [doi:10.1063/1.3560091]