Noncovalent Interactions by 1-Determinant Fixed-Node Diffusion Monte Carlo


Fixed-node diffusion Monte Carlo (FNDMC) is a many-body electronic structure approach promising for its accuracy, massive parallelism, low-order polynomial CPU cost scaling, and, direct treatment of extended systems. For computational reasons, FNDMC is most often used with 1-determinant trial wave functions that introduce FN bias which is hardly under control. In the limit of weak interaction, the FN bias cancels out and FNDMC attains sub-kJ accuracy (vs. CCSD(T)/CBS) in small trivially saturated s/p complexes even with far-from-exact trial wave functions. The primary goal of this project is to extend our understanding of 1-determinant FNDMC limits in complex low-dimensional noncovalent systems by screening possible bias sources. On the application side, reference computations will include representative classes of nontrivial noncovalent systems like, e.g., infinite 1D chains of hydrogen-bonds.

Chemical Physics
Vedecká časť: 

Noncovalent interactions (NCI) are crucial in many areas of research, including, e.g., materials science or drug design and their importance can hardly be overemphasized. Their accurate modeling, providing valuable insights complementary to experiments, poses a serious challenge to modern computational disciplines. Interest in large-scale models motivates development of scalable methods, that rely on quantum-mechanical benchmarks. However, the current demands on benchmark methods (e.g. size of large supramolecular complexes or extended systems) can only hardly be addressed by the conventional approaches, like coupled-cluster, that suffer from prohibitive CPU cost, inefficient parallelism, and/or lack of native description of periodicity.

Fixed-node diffusion Monte Carlo (FNDMC) is a many-body electronic structure quantum Monte Carlo (QMC) method that may complement such benchmark methodologies for its accuracy, direct treatment of periodicity, low-order polynomial CPU cost scaling, and massive parallelism [1].

It was shown only recently, that 1-determinant FNDMC is able to compete with the high standard of quantum chemistry (CCSD(T)/CBS) [2] to an astonishing level of accuracy (0.1 kcal/mol). This success was attributed to a high degree of FN bias cancellation, operative in the limit of sufficiently weak intermolecular interactions, where Pauli repulsion is negligible. This makes FNDMC a promising choice for benchmarks in large models, where it has no competitors. E.g., large host-guest complexes [3] of the order of 100 atoms clearly show that the size-limits of FNDMC are far beyond the possibilities of CCSD(T) or even MP2. However, limits of such 1-determinant FNDMC approaches are not yet exhaustively understood and clearly defined, that prevents their wide usage. E.g., deviations of FNDMC from CCSD(T)/CBS in hydrogen-bond complexes containing double and triple bonds (HCN dimer or formaldehyde dimer) delineate limits of this approach[4]. In addition, only little is known about the possible tradeoffs in periodic setting.

There is now an urgent need for more systematic understanding of 1-determinant FNDMC biases, and, development of more effective universal (or system-specific) computational protocols with guaranteed level of accuracy[1]. To this end, in this project, two important independent related tasks will be performed:

A) large-scale computer-aided mapping of 1-determinant FNDMC biases; this will be performed on a set of small noncovalent models and screening will include some of the to-date undervalued technical parameters of FNDMC (size-consistency, decomposition of FN and ECP error), and, more importantly, bond multiplicities of molecular cluster constituents (e.g. single vs. double bonds), dimensionality of noncovalent contacts (molecule-molecule, molecule-1D wire, etc.), accuracy in presence of open-shells, and possibly other variables. This will facilitate development of a conceptual understanding of bias sources (and possible alleviations) and new generation of versatile black-box FNDMC-based protocol/s with certified accuracy level/s, that are now unavailable.

B) landmark benchmarks of low-dimensional extended noncovalent systems; representative classes of technologically or fundamentally important systems from A) where 1-determinant FNDMC would provide benchmark accuracy, e.g. binding energies of 1D crystals of small trivially saturated molecules, will be computed.

[1] M. Dubecky, et al.: Chem. Rev., 116, 5188, 2016.
[2] M. Dubecky, et al.: J. Chem. Theory Comput., 9 ,4287, 2013.
[3] A. Ambrosetti, D. Alfe, R. A. DiStasio Jr., and A. Tkatchenko. J. Phys. Chem. Lett., 5, 849–855, 2014.
[4] M. Dubecky, et al.: Phys. Chem. Chem. Phys., 16, 20915, 2014.

Socioekonomický a technologický dopad: 

QMC is expected to play increasingly more important role in nanotechnology research with the advent of massively parallel peta-flop supercomputers and multiprocessor architectures in future. With respect to short history of QMC, especially in area of noncovalent interactions (2003), it can still be considered as a newcomer, and, clearly, a lot of work remains to be done. In this respect, the objectives of out project are very timely and their accomplishment would make a huge and long-standing impact.

More specifically, the computer aided mapping of errors will contribute to development of a comprehensive map of FNDMC limitations, including the step-wise dependence on the dimensionality of a noncovalent contact. The new FNDMC protocols with certified error bounds, together with the development of conceptual understanding of the physics behind, will guide FNDMC users toward the right methods for right reasons. The produced representative benchmarks (applications) will serve as a proof-of-principle.

The project outputs will be published in the renowned journals.

Technická časť: 

The large-scale FNDMC calculations will use the software quantum Monte Carlo code QWalk ( All systems will use trial wave functions based on Dunning-type Gaussian basis sets, DFT/B3LYP orbitals (from GAMESS or SIESTA), two- or three-body explicit correlation Jastrow terms with up to electron-electron-nucleus terms will be considered. FNDMC will use a default timestep of 0.005 a.u. and tests with smaller values for d electrons will be performed within the project. The so-called T-moves approximation will be used as a default setting for the treatment of effective-core potentials.

This project is a part of the long-term effort and as such, it expects consumption at least 400k CPUhours for the part A) and the benchmark part, B), expects consumption of at least 300k CPUhours in 2017.

M. Dubecky, et al.: J. Chem. Theory Comput., 9 ,4287, 2013
J. Granatier, M. Dubecky, et al. J. Chem. Theory Comput. 9, 1461, 2013
F. Karlicky, P. Lazar, M. Dubecky, M. Otyepka: J. Chem. Theory Comput., 9, 3670, 2013
M. Dubecky, et al.: Phys. Chem. Chem. Phys., 16, 20915, 2014
M. Dubecky: J. Chem. Theory Comput. 13, 3626, 2017