  In this work, we introduce three algorithmic improvements to reduce the cost
and improve the scaling of orbital space variational Monte Carlo (VMC). First,
we show that by appropriately screening the one- and two-electron integrals of
the Hamiltonian one can improve the efficiency of the algorithm by several
orders of magnitude. This improved efficiency comes with the added benefit that
the resulting algorithm scales as the second power of the system size $O(N^2)$,
down from the fourth power $O(N^4)$. Using numerical results, we demonstrate
that the practical scaling obtained is in fact $O(N^{1.5})$ for a chain of
Hydrogen atoms, and $O(N^{1.2})$ for the Hubbard model. Second, we introduce
the use of the rejection-free continuous time Monte Carlo (CTMC) to sample the
determinants. CTMC is usually prohibitively expensive because of the need to
calculate a large number of intermediates. Here, we take advantage of the fact
that these intermediates are already calculated during the evaluation of the
local energy and consequently, just by storing them one can use the CTCM
algorithm with virtually no overhead. Third, we show that by using the adaptive
stochastic gradient descent algorithm called AMSGrad one can optimize the
wavefunction energies robustly and efficiently. The combination of these three
improvements allows us to calculate the ground state energy of a chain of 160
hydrogen atoms using a wavefunction containing $\sim 2\times 10^5$ variational
parameters with an accuracy of 1 $mE_h$/particle at a cost of just 25 CPU
hours, which when split over 2 nodes of 24 processors each amounts to only
about half hour of wall time. This low cost coupled with embarrassing
parallelizability of the VMC algorithm and great freedom in the forms of usable
wavefunctions, represents a highly effective method for calculating the
electronic structure of model and \emph{ab initio} systems.
