Download non-born–oppenheimer effects between electrons and protons

BLUE WATERS ANNUAL REPORT
NON-BORN–OPPENHEIMER
EFFECTS BETWEEN ELECTRONS
AND PROTONS
Allocation: BW Prof/0.24 Mnh
PI: Sharon Hammes-Schiffer1
1
University of Illinois at Urbana-Champaign
EXECUTIVE SUMMARY:
The quantum mechanical behavior of nuclei plays
an important role in a wide range of chemical
and biological processes. The inclusion of nuclear
quantum effects and non-Born–Oppenheimer
effects between nuclei and electrons in computer
simulations is challenging. Our group has
developed the nuclear-electronic orbital (NEO)
method for treating electrons and select nuclei in
a quantum mechanical manner on the same level
using an orbital-based formalism. The NEO code
uses a hybrid MPI/OpenMP protocol, but the
calculations require a large number of processors
and a substantial amount of memory. We have
used Blue Waters to perform NEO calculations
on systems in which all electrons and one proton
are treated quantum mechanically and have
tested approximate methods that enable the
study of larger systems.
INTRODUCTION
The inclusion of nuclear quantum effects such
as zero-point energy and tunneling in electronic
structure calculations is important for the study
of a variety of chemical systems, particularly
those involving hydrogen transfer or hydrogenbonding interactions. Moreover, non-adiabatic
effects, also called non-Born–Oppenheimer
effects, between electrons and certain nuclei
are significant for many of these systems. In
this case, the electrons cannot be assumed to
respond instantaneously to the nuclear motions,
and the concept of the nuclei moving on a single
electronic potential energy surface is no longer
valid. This type of non-adiabaticity has been
shown to play a critical role in proton-coupled
electron transfer (PCET) reactions, which
are essential for a wide range of chemical and
biological processes, including photosynthesis,
respiration, enzyme reactions, and energy devices
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such as solar cells. The development of non-Born–
Oppenheimer methods to enable accurate and
efficient calculations of PCET reactions will
impact many scientific endeavors, from drug
design to the design of more effective catalysts
for solar energy devices.
METHODS AND RESULTS
In the NEO approach, typically all electrons
and one or a few protons are treated quantum
mechanically, and a mixed nuclear-electronic
time-independent Schrödinger equation is
solved. To include the essential electron-proton
correlation, we developed an explicitly correlated
method, denoted NEO-XCHF. Although
explicitly correlated methods have been shown
to be highly accurate for model systems, they
are computationally expensive and are currently
intractable for larger systems of chemical interest.
Recently, we proposed an alternative ansatz
with the primary goal of improving computational
tractability to enable the study of larger systems
of chemical interest. In this approach, denoted
NEO-RXCHF, only select electronic orbitals
are explicitly correlated to the nuclear orbital(s)
and certain exchange terms are approximated,
thereby substantially decreasing the number of
multi-particle integrals that must be calculated.
The computational bottleneck is the calculation
of two-, three-, and four-particle integrals that
arise from computing matrix elements of the
explicitly correlated wave function over the
mixed nuclear-electronic Hamiltonian. Since
these integrals can be calculated completely
independently from one another we applied
the OpenMP protocol, providing almost perfect
scaling with respect to the number of threads.
When considering calculations on larger
proton-containing systems, two drawbacks with
the shared-memory-based OpenMP model are
of immediate concern: (1) the parallelization is
restricted to the number of cores on a single
machine, which is usually 32 at most, and (2)
the calculations must be performed using the
memory of a single machine. A hybrid MPI/
OpenMP protocol obviates the need for all
integrals to be stored simultaneously and allows
the division of the calculation over different
machines. This version of the code scales very
well with respect to the number of MPI processes.
We performed initial NEO-RXCHF
calculations on proton-containing systems on
Blue Waters. We analyzed the nuclear densities
of the protons and compared them to highly
accurate grid-based densities. Our calculations
illustrate that this approach can provide accurate
descriptions of the protons that are treated
quantum mechanically. We also have tested new
approximate methods that will enable the study of
larger proton-containing systems. Current work
focuses on refining these approximate methods
and investigating larger systems of chemical and
biological interest. Our long-term objective is
to use these non-Born–Oppenheimer methods
to study PCET in molecular catalysts that are
directly relevant to solar energy conversion.
WHY BLUE WATERS
Our in-house NEO code has been adapted
to incorporate a hybrid MPI/OpenMP protocol,
but the calculations require a large number of
processors and a substantial amount of memory.
The highly parallel computing system on Blue
Waters is essential for the application of this
approach to systems of interest, where the
computational bottleneck is the embarrassingly
parallelizable calculation of many integrals. Most
importantly, the large memory requirements
of storing these integrals render this problem
impossible when a large number of nodes cannot
be used simultaneously, as on other computer
systems. As our code has demonstrated excellent
scaling, we are able to directly benefit from using
a large number of nodes simultaneously on Blue
Waters with very little overhead.
FIGURE 1: The results of a NEO-RXCHF calculation
performed on the hydrogen cyanide molecule. (Top)
Correlated electron and proton molecular orbitals
obtained from the NEO calculation. The electron
orbital is shown in green and purple, indicating
its two phases, and the proton orbital is shown
in red. (Bottom) The proton density along the N-C-H
axis, comparing the results of the NEO calculation
(red dashed) to a numerically exact benchmark gridbased calculation (black solid).
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