6 research outputs found

### <i>Ab Initio</i> Molecular Dynamics Using Recursive, Spatially Separated, Overlapping Model Subsystems Mixed within an ONIOM-Based Fragmentation Energy Extrapolation Technique

Here,
we demonstrate the application of fragment-based electronic
structure calculations in (a) <i>ab initio</i> molecular
dynamics (AIMD) and (b) reduced dimensional potential calculations,
for medium- and large-sized protonated water clusters. The specific
fragmentation algorithm used here is derived from ONIOM, but includes
multiple, overlapping âmodelâ systems. The interaction
between the various overlapping model systems is (a) approximated
by invoking the principle of inclusion-exclusion at the chosen higher
level of theory and (b) within a real calculation performed at the
chosen lower level of theory. The fragmentation algorithm itself is
written using bit-manipulation arithmetic, which will prove to be
advantageous, since the number of fragments in such methods has the
propensity to grow exponentially with system size. Benchmark calculations
are performed for three different protonated water clusters: H<sub>9</sub>O<sub>4</sub><sup>+</sup>,
H<sub>13</sub>O<sub>6</sub><sup>+</sup> and HÂ(H<sub>2</sub>O)<sub>21</sub><sup>+</sup>. For potential energy surface benchmarks, we sample the normal
coordinates and compare our surface energies with full MP2 and CCSDÂ(T)
calculations. The mean absolute error for the fragment-based algorithm
is <0.05 kcal/mol, when compared with MP2 calculations, and <0.07
kcal/mol, when compared with CCSDÂ(T) calculations over 693 different
geometries for the H<sub>9</sub>O<sub>4</sub><sup>+</sup> system. For the larger HÂ(H<sub>2</sub>O)<sub>21</sub><sup>+</sup> water cluster,
the mean absolute error is on the order of a 0.1 kcal/mol, when compared
with full MP2 calculations for 84 different geometries, at a fraction
of the computational cost. <i>Ab initio</i> dynamics calculations
were performed for H<sub>9</sub>O<sub>4</sub><sup>+</sup> and H<sub>13</sub>O<sub>6</sub><sup>+</sup>, and the energy conservation was found
to be of the order of 0.01 kcal/mol for short trajectories (on the
order of a picosecond). The trajectories were kept short because our
algorithm does not currently include dynamical fragmentation, which
will be considered in future publications. Nevertheless, the velocity
autocorrelation functions and their Fourier transforms computed from
the fragment-based AIMD approaches were found to be in excellent agreement
with those computed using the respective higher level of theory from
the chosen hybrid calculation

### A Multiwavelet Treatment of the Quantum Subsystem in Quantum Wavepacket <i>Ab Initio</i> Molecular Dynamics through an Hierarchical Partitioning of Momentum Space

We
present an hierarchical scheme where the propagator in quantum
dynamics is represented using a multiwavelet basis. The approach allows
for a recursive refinement methodology, where the representation in
momentum space can be adaptively improved through additional, decoupled
layers of basis functions. The method is developed within the constructs
of quantum-wavepacket ab initio molecular dynamics (QWAIMD), which
is a quantum-classical method and involves the synergy between a time-dependent
quantum wavepacket description and ab initio molecular dynamics. Specifically,
the current development is embedded within an âon-the-flyâ
multireference electronic structural generalization of QWAIMD. The
multiwavelet treatment is used to study the dynamics and spectroscopy
in a small hydrogen bonded cluster. The results are in agreement with
previous calculations and with experiment. The studies also allow
an interpretation of the shared proton dynamics as one that can be
modeled through the dynamics of dressed states

### Constructing Periodic Phase Space Orbits from <i>ab Initio</i> Molecular Dynamics Trajectories to Analyze Vibrational Spectra: Case Study of the Zundel (H<sub>5</sub>O<sub>2</sub><sup>+</sup>) Cation

A method of analysis is introduced to probe the spectral
features obtained from <i>ab initio</i> molecular dynamics
simulations. Here, the instantaneous mass-weighted velocities are
projected onto irreducible representations constructed from discrete
time translation groups comprising operations that invoke the time-domain
symmetries (or periodic phase space orbits) reflected in the spectra.
The projected velocities are decomposed using singular value decomposition
(SVD) to construct a set of âmodesâ pertaining to a
given frequency domain. These modes now include all anharmonicities,
as sampled during the dynamics simulations. In this approach, the
underlying motions are probed in a manner invariant with respect to
coordinate transformations, operations being performed along the time
axis rather than coordinate axes, making the analysis independent
of choice of reference frame. The method is used to probe the underlying
motions responsible for the doublet at âŒ1000 cm<sup>â1</sup> in the vibrational spectrum of the H<sub>5</sub>O<sub>2</sub><sup>+</sup>, Zundel cation. The associated analysis results are confirmed
by projecting the Fourier transformed velocities onto the harmonic
normal mode coordinates and a set of mass-weighted, symmetrized Jacobi
coordinates. It is found that the two peaks of the doublet are described
and differentiated by their respective contributions from the proton
transfer, waterâwater stretch, and water wag coordinates, as
these are defined. Temperature dependent effects are also briefly
noted

### Efficient, âOn-the-Flyâ, BornâOppenheimer and CarâParrinello-type Dynamics with Coupled Cluster Accuracy through Fragment Based Electronic Structure

We recently developed two fragment
based <i>ab initio</i> molecular dynamics methods, and in
this publication we have demonstrated
both approaches by constructing efficient classical trajectories in
agreement with trajectories obtained from âon-the-flyâ
CCSD. The dynamics trajectories are obtained using both BornâOppenheimer
and extended Lagrangian (CarâParrinello-style) options, and
hence, here, for the first time, we present CarâParrinello-like
AIMD trajectories that are accurate to the CCSD level of post-HartreeâFock
theory. The specific extended Lagrangian implementation used here
is a generalization to atom-centered density matrix propagation (ADMP)
that provides post-HartreeâFock accuracy, and hence the new
method is abbreviated as ADMP-pHF; whereas the BornâOppenheimer
version is called frag-BOMD. The fragmentation methodology is based
on a set-theoretic, inclusion-exclusion principle based generalization
of the well-known ONIOM method. Thus, the fragmentation scheme contains
multiple overlapping âmodelâ systems, and overcounting
is compensated through the inclusion-exclusion principle. The energy
functional thus obtained is used to construct BornâOppenheimer
forces (frag-BOMD) and is also embedded within an extended Lagrangian
(ADMP-pHF). The dynamics is tested by computing structural and vibrational
properties for protonated water clusters. The frag-BOMD trajectories
yield structural and vibrational properties in excellent agreement
with full CCSD-based âon-the-flyâ BOMD trajectories,
at a small fraction of the cost. The asymptotic (large system) computational
scaling of both frag-BOMD and ADMP-pHF is inferred as O(N3.5), for on-the-fly CCSD accuracy. The extended
Lagrangian implementation, ADMP-pHF, also provides structural features
in excellent agreement with full âon-the-flyâ CCSD calculations,
but the dynamical frequencies are slightly red-shifted. Furthermore,
we study the behavior of ADMP-pHF as a function of the electronic
inertia tensor and find a monotonic improvement in the red-shift as
we reduce the electronic inertia. In all cases a uniform spectral
scaling factor, that in our preliminary studies appears to be independent
of system and independent of level of theory (same scaling factor
for both MP2 and CCSD implementations ADMP-pHF and for ADMP DFT),
improves on agreement between ADMP-pHF and full CCSD calculations.
Hence, we believe both frag-BOMD and ADMP-pHF will find significant
utility in modeling complex systems. The computational power of frag-BOMD
and ADMP-pHF is demonstrated through preliminary studies on a much
larger protonated 21-water cluster, for which AIMD trajectories with
âon-the-flyâ CCSD are not feasible

### Gauging the Flexibility of the Active Site in Soybean Lipoxygenaseâ1 (SLO-1) through an Atom-Centered Density Matrix Propagation (ADMP) Treatment That Facilitates the Sampling of Rare Events

We present a computational methodology to sample rare
events in large biological enzymes that may involve electronically
polarizing, reactive processes. The approach includes simultaneous
dynamical treatment of electronic and nuclear degrees of freedom,
where contributions from the electronic portion are computed using
hybrid density functional theory and the computational costs are reduced
through a hybrid quantum mechanics/molecular mechanics (QM/MM) treatment.
Thus, the paper involves a QM/MM dynamical treatment of rare events.
The method is applied to probe the effect of the active site elements
on the critical hydrogen transfer step in the soybean lipoxygenase-1
(SLO-1) catalyzed oxidation of linoleic acid. It is found that the
dynamical fluctuations and associated flexibility of the active site
are critical toward maintaining the electrostatics in the regime where
the reactive process can occur smoothly. Physical constraints enforced
to limit the active site flexibility are akin to mutations and, in
the cases studied, have a detrimental effect on the electrostatic
fluctuations, thus adversely affecting the hydrogen transfer process

### Adaptive, Geometric Networks for Efficient Coarse-Grained <i>Ab Initio</i> Molecular Dynamics with Post-HartreeâFock Accuracy

We
introduce a new coarse-graining technique for <i>ab initio</i> molecular dynamics that is based on the adaptive generation of connected
geometric networks or graphs specific to a given molecular geometry.
The coarse-grained nodes depict a local chemical environment and are <i>networked</i> to create edges, triangles, tetrahedrons, and
higher order simplexes based on (a) a Delaunay triangulation procedure
and (b) a method that is based on molecular, bonded and nonbonded,
local interactions. The geometric subentities thus created, that is
nodes, edges, triangles, and tetrahedrons, each represent an energetic
measure for a specific portion of the molecular system, capturing
a specific set of interactions. The energetic measure is constructed
in a manner consistent with ONIOM and allows assembling an overall
molecular energy that is purely based on the geometric network derived
from the molecular conformation. We use this approach to obtain accurate
MP2 energies for polypeptide chains containing up to 12 amino-acid
monomers (123 atoms) and DFT energies up to 26 amino-acid monomers
(263 atoms). The energetic measures are obtained at much reduced computational
costs; the approach currently yields MP2 energies at DFT cost and
DFT energies at PM6 cost. Thus, in essence the method performs an
efficient âcoarse-grainingâ of the molecular system
to accurately reproduce the electronic structure properties. The method
is comparable in principle to several fragmentation procedures recently
introduced in the literature, including previous procedures introduced
by two of the authors here, but critically differs by overcoming the
computational bottleneck associated with adaptive fragment creation
without spatial cutoffs. The method is used to derive a new, efficient,
ab initio molecular dynamics formalism (both BornâOppenheimer
and CarâParrinello-style extended Lagrangian schemes are presented)
a critical hallmark of which is that, at each dynamics time-step,
multiple electronic structure packages can be simultaneously invoked
to assemble the energy and forces for the full system. Indeed, in
this paper, as an illustration, we use both Psi4 and Gaussian09 simultaneously
at every time-step to perform AIMD simulations and also the energetic
benchmarks. The approach works in parallel (currently over 100 processors),
and the computational implementation is object oriented in C++. MP2 and DFT based on-the-fly
dynamics results are recovered to good accuracy from the coarse-grained
AIMD methods introduced here at reduced costs as highlighted above