193 research outputs found
Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions
We present an investigation into the use of an explicitly correlated plane
wave basis for periodic wavefunction expansions at the level of second-order
M{\o}ller-Plesset perturbation theory (MP2). The convergence of the electronic
correlation energy with respect to the one-electron basis set is investigated
and compared to conventional MP2 theory in a finite homogeneous electron gas
model. In addition to the widely used Slater-type geminal correlation factor,
we also derive and investigate a novel correlation factor that we term
Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic
results for two electrons in a box and allows for a further improved
convergence of the correlation energies with respect to the employed basis set.
We find the combination of the infinitely delocalized plane waves and local
short-ranged geminals provides a complementary, and rapidly convergent basis
for the description of periodic wavefunctions. We hope that this approach will
expand the scope of discrete wavefunction expansions in periodic systems.Comment: 15 pages, 13 figure
A regularized second-order correlation method from Green's function theory
We present a scalable single-particle framework to treat electronic
correlation in molecules and materials motivated by Green's function theory. We
derive a size-extensive Brillouin-Wigner perturbation theory from the
single-particle Green's function by introducing the Goldstone self-energy. This
new ground state correlation energy, referred to as Quasi-Particle MP2 theory
(QPMP2), avoids the characteristic divergences present in both second-order
M{\o}ller-Plesset perturbation theory (MP2) and Coupled Cluster Singles and
Doubles (CCSD) within the strongly correlated regime. We show that the exact
ground state energy and properties of the Hubbard dimer are reproduced by QPMP2
and demonstrate the advantages of the approach for the six-, eight- and
ten-site Hubbard models where the metal-to-insulator transition is
qualitatively reproduced, contrasting with the complete failure of traditional
methods. We apply this formalism to characteristic strongly correlated
molecular systems and show that QPMP2 provides an efficient, size-consistent
regularization of MP2
The coupled-cluster self-energy
An improved description of electronic correlation in molecules and materials
can only be achieved by uncovering connections between different areas of
electronic structure theory. A general unifying relationship between the
many-body self-energy and coupled-cluster theory has remained hitherto unknown.
Here, we present a formalism for constructing the coupled-cluster self-energy
from the coupled-cluster ground state energy. Our approach illuminates the
fundamental connections between the many-body self-energy and the
coupled-cluster equations. As a consequence, we naturally arrive at the
coupled-cluster quasiparticle and Bethe-Salpeter equations describing
correlated electrons and excitons. This deep underlying structure explains the
origin of the connections between RPA, -BSE and coupled-cluster theory,
whilst also elucidating the relationship between vertex corrections and the
amplitude equations
Improved CPS and CBS Extrapolation of PNO-CCSD(T) Energies: The MOBH35 and ISOL24 Data Sets
Computation of heats of reaction of large molecules is now feasible using
domain-based PNO-CCSD(T) theory. However, to obtain agreement within 1~kcal/mol
of experiment, it is necessary to eliminate basis set incompleteness error,
which comprises of both the AO basis set error and the PNO truncation error.
Our investigation into the convergence to the canonical limit of PNO-CCSD(T)
energies with PNO truncation threshold shows that errors follow the model
. Therefore, PNO truncation errors can be eliminated
using a simple two-point CPS extrapolation to the canonical limit, so that
subsequent CBS extrapolation is not limited by residual PNO truncation error.
Using the ISOL24 and MOBH35 data sets, we find that PNO truncation errors are
larger for molecules with significant static correlation, and that it is
necessary to use very tight thresholds of to ensure errors do not
exceed 1~kcal/mol. We present a lower-cost extrapolation scheme that uses
information from small basis sets to estimate PNO truncation errors for larger
basis sets. In this way the canonical limit of CCSD(T) calculations on large
molecules with large basis sets can be reliably estimated in a practical way.
Using this approach, we report complete basis set limit CCSD(T) reaction
energies for the full ISOL24 and MOBH35 data sets
Exact electronic states with shallow quantum circuits from global optimisation
Quantum computers promise to revolutionise molecular electronic simulations by overcoming the exponential memory scaling. While electronic wave functions can be represented using a product of fermionic unitary operators, the best ansatz for strongly correlated electronic systems is far from clear. In this contribution, we construct universal wave functions from gate-efficient, spin symmetry-preserving fermionic operators by introducing an algorithm that globally optimises the wave function in the discrete ansatz design and continuous parameter spaces. Our approach maximises the accuracy that can be obtained with near-term quantum circuits and provides a practical route for designing ansätze in the future. Numerical simulations for strongly correlated molecules, including water and molecular nitrogen, and the condensed-matter Hubbard model, demonstrate the improved accuracy of gate-efficient quantum circuits for simulating strongly correlated chemistry
Ab initio instanton rate theory made efficient using Gaussian process regression
Ab initio instanton rate theory is a computational method for rigorously
including tunnelling effects into calculations of chemical reaction rates based
on a potential-energy surface computed on the fly from electronic-structure
theory. This approach is necessary to extend conventional transition-state
theory into the deep-tunnelling regime, but is also more computationally
expensive as it requires many more ab initio calculations. We propose an
approach which uses Gaussian process regression to fit the potential-energy
surface locally around the dominant tunnelling pathway. The method can be
converged to give the same result as from an on-the-fly ab initio instanton
calculation but requires far fewer electronic-structure calculations. This
makes it a practical approach for obtaining accurate rate constants based on
high-level electronic-structure methods. We show fast convergence to reproduce
benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in
full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.Comment: 12 pages, 4 figures; submitted to Faraday Discussion: Quantum effects
in small molecular system
Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip
Quantum phase estimation is a fundamental subroutine in many quantum
algorithms, including Shor's factorization algorithm and quantum simulation.
However, so far results have cast doubt on its practicability for near-term,
non-fault tolerant, quantum devices. Here we report experimental results
demonstrating that this intuition need not be true. We implement a recently
proposed adaptive Bayesian approach to quantum phase estimation and use it to
simulate molecular energies on a Silicon quantum photonic device. The approach
is verified to be well suited for pre-threshold quantum processors by
investigating its superior robustness to noise and decoherence compared to the
iterative phase estimation algorithm. This shows a promising route to unlock
the power of quantum phase estimation much sooner than previously believed
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