arXiv subjects

Ali Alavi

Publications and source records attributed to Ali Alavi.

At least 91 records · Page 5Linked to original sources

arXiv2018

Full configuration interaction quantum Monte Carlo benchmark and multireference coupled cluster studies of tetramethyleneethane diradical

We have performed a FCI-quality benchmark calculation for the tetramethyleneethane molecule in cc-pVTZ basis set employing a subset of CASPT2(6,6) natural orbitals for the FCIQMC calculation. The results are in an excellent agreement with the previous large scale diffusion Monte Carlo calculations by Pozun et al. and available experimental results. Our computations verified that there is a maximum on PES of the ground singlet state ($^1\text{A}$) $45^{\circ}$ torsional angle and the corresponding vertical singlet-triplet energy gap is $0.01$ eV. We have employed this benchmark for assessment of the accuracy of MkCCSDT and DMRG-tailored CCSD (TCCSD) methods. MR MkCCSDT with CAS(2,2) model space, though giving good values for the singlet-triplet energy gap, is not able to properly describe the shape of the multireference singlet PES. Similarly, DMRG(24,25) is not able to correctly capture the shape of the singlet surface, due to the missing dynamic correlation. On the other hand, the DMRG-tailored CCSD method describes the shape of the ground singlet state with an excellent accuracy, but for the correct ordering requires computation of the zero-spin-projection component of the triplet state ($^3\text{B}_1$).

physics.chem-ph↗

arXiv2017

Understanding the mechanism stabilizing intermediate spin states in Fe(II)-Porphyrin

Spin fluctuations in Fe(II)-porphyrins are at the heart of heme-proteins functionality. Despite significant progress in porphyrin chemistry, the mechanisms that rule spin state stabilisation remain elusive. Here, it is demonstrated by using multiconfigurational quantum chemical approaches, including the novel Stochastic-CASSCF method, that electron delocalization between the metal centre and the pi system of the macrocycle differentially stabilises the triplet spin states over the quintet. This delocalisation takes place via charge-transfer excitations, involving the out-of-plane iron d orbitals, key linking orbitals between metal and macrocycle. Through a correlated breathing mechanism, the 3d electrons can make transitions towards the pi orbitals of the macrocycle. This guarantees a strong coupling between the on-site radial correlation on the metal and electron delocalization. Opposite-spin 3d electrons of the triplet can effectively reduce electron repulsion in this manner. Constraining the out-of-plane orbitals from breathing hinders delocalization and reverses the spin ordering. Our results find a qualitative analogue in Kekulé resonance structures involving also the metal centre.

physics.chem-ph↗

arXiv2017

Density matrices in full configuration interaction quantum Monte Carlo: Excited states, transition dipole moments and parallel distribution

We present developments in the calculation of reduced density matrices (RDMs) in the full configuration interaction quantum Monte Carlo (FCIQMC) method. An efficient scheme is described to allow storage of RDMs across distributed memory, thereby allowing their calculation and storage in large basis sets. We demonstrate the calculation of RDMs for general states by using the recently-introduced excited-state FCIQMC approach [J. Chem. Phys. 143, 134117 (2015)] and further introduce calculation of transition density matrices (TDMs) in the method. These approaches are combined to calculate excited-state dipole and transition dipole moments for heteronuclear diatomic molecules, including LiH, BH and MgO, and initiator error is investigated in these quantities.

physics.comp-ph↗

arXiv2017

Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory

We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 12, 3674 (2016)], by introducing a semistochastic algorithm for performing multireference Epstein-Nesbet perturbation theory, in order to completely eliminate the severe memory bottleneck of the original method. The proposed algorithm has several attractive features. First, there is no sign problem that plagues several quantum Monte Carlo methods. Second, instead of using Metropolis-Hastings sampling, we use the Alias method to directly sample determinants from the reference wavefunction, thus avoiding correlations between consecutive samples. Third, in addition to removing the memory bottleneck, semistochastic HCI (SHCI) is faster than the deterministic variant for many systems if a stochastic error of 0.1 mHa is acceptable. Fourth, within the SHCI algorithm one can trade memory for a modest increase in computer time. Fifth, the perturbative calculation is embarrassingly parallel. The SHCI algorithm extends the range of applicability of the original algorithm, allowing us to calculate the correlation energy of very large active spaces. We demonstrate this by performing calculations on several first row dimers including F2 with an active space of (14e, 108o), Mn-Salen cluster with an active space of (28e, 22o), and Cr2 dimer with up to a quadruple-zeta basis set with an active space of (12e, 190o). For these systems we were able to obtain better than 1 mHa accuracy with a wall time of merely 55 seconds, 37 seconds, and 56 minutes on 1, 1, and 4 nodes, respectively.

physics.chem-ph↗

arXiv2016

Stochastic multi-reference perturbation theory with application to linearized coupled cluster method

In this article we report a stochastic evaluation of the recently proposed LCC multireference perturbation theory [Sharma S., and Alavi A., J. Chem. Phys. 143, 102815, (2015)]. In this method both the zeroth order and first order wavefunctions are sampled stochastically by propagating simultaneously two populations of signed walkers. The sampling of the zeroth order wavefunction follows a set of stochastic processes identical to the one used in the FCIQMC method. To sample the first order wavefunction, the usual FCIQMC algorithm is augmented with a source term that spawns walkers in the sampled first order wavefunction from the zeroth order wavefunction. The second order energy is also computed stochastically but requires no additional overhead outside of the added cost of sampling the first order wavefunction. This fully stochastic method opens up the possibility of simultaneously treating large active spaces to account for static correlation and recovering the dynamical correlation using perturbation theory. This method is used to study a few benchmark systems including the carbon dimer and aromatic molecules. We have computed the singlet-triplet gaps of benzene and m-xylylene. For m-xylylene, which has proved difficult for standard CASSCF+PT, we find the singlet-triplet gap to be in good agreement with the experimental values.

physics.chem-ph↗

arXiv2016

Combining internally contracted states and matrix product states to perform multireference perturbation theory

We present two efficient and intruder-free methods for treating dynamic correlation on top of general multi-configuration reference wave functions---including such as obtained by the density matrix renormalization group (DMRG) with large active spaces. The new methods are the second order variant of the recently proposed multi-reference linearized coupled cluster method (MRLCC) [S. Sharma, A. Alavi, J. Chem. Phys. 143, 102815 (2015)], and of N-electron valence perturbation theory (NEVPT2), with expected accuracies similar to MRCI+Q and (at least) CASPT2, respectively. Great efficiency gains are realized by representing the first-order wave function with a combination of internal contraction (IC) and matrix product state perturbation theory (MPSPT). With this combination, only third order reduced density matrices (RDMs) are required. Thus, we obviate the need for calculating (or estimating) RDMs of fourth or higher order; these had so far posed a severe bottleneck for dynamic correlation treatments involving the large active spaces accessible to DMRG. Using several benchmark systems, including first and second row containing small molecules, Cr$_2$, pentacene and oxo-Mn(Salen), we shown that active spaces containing at least 30 orbitals can be treated using this method. On a single node, MRLCC2 and NEVPT2 calculations can be performed with over 550 and 1100 virtual orbitals, respectively. We also critically examine the errors incurred due to the three sources of errors introduced in the present implementation - calculating second order instead of third order energy corrections, use of internal contraction and approximations made in the reference wavefunction due to DMRG.

physics.chem-ph↗

arXiv2016

Assessment of Multireference Approaches to Explicitly Correlated Full Configuration Interaction Quantum Monte Carlo

The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schrödinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansion of Slater determinants, the FCIQMC method suffers from a basis set incompleteness error that decays very slowly with the size of the employed single particle basis. The FCIQMC results obtained in a small basis set can be improved significantly with explicitly correlated techniques. Here, we present a study that assesses and compares two contrasting `universal' explicitly correlated approaches that fit into the FCIQMC framework; the $[2]_{R12}$ method of Valeev {\em et al.}, and the explicitly correlated canonical transcorrelation approach of Yanai {\em et al}. The former is an {\em a posteriori} internally-contracted perturbative approach, while the latter transforms the Hamiltonian prior to the FCIQMC simulation. These comparisons are made across the 55 molecules of the G1 standard set. We found that both methods consistently reduce the basis set incompleteness, for accurate atomization energies in small basis sets, reducing the error from 28~mE$_{\text h}$ to 3-4~mE$_{\text h}$. While many of the conclusions hold in general for any combination of multireference approaches with these methodologies, we also consider FCIQMC-specific advantages of each approach.

physics.comp-ph↗

arXiv2015

Stochastic multi-configurational self-consistent field theory

The multi-configurational self-consistent field theory is considered the standard starting point for almost all multireference approaches required for strongly-correlated molecular problems. The limitation of the approach is generally given by the number of strongly-correlated orbitals in the molecule, as its cost will grow exponentially with this number. We present a new multi-configurational self-consistent field approach, wherein linear determinant coefficients of a multi-configurational wavefunction are optimized via the stochastic full configuration interaction quantum Monte Carlo technique at greatly reduced computational cost, with non-linear orbital rotation parameters updated variationally based on this sampled wavefunction. This extends this approach to strongly-correlated systems with far larger active spaces than it is possible to treat by conventional means. By comparison with this traditional approach, we demonstrate that the introduction of stochastic noise in both the determinant amplitudes and the gradient and Hessian of the orbital rotations does not preclude robust and reliable convergence of the orbital optimization. It can even improve the ability to avoid convergence to local minima in the orbital space, and therefore aid in finding variationally lower-energy solutions. We consider the effect on the convergence of the orbitals as the number of walkers and the sampling time within the active space increases, as well as the effect on the final energy and error. The scope of the new protocol is demonstrated with a study of the increasingly strongly correlated electronic structure in a series of polycyclic aromatic hydrocarbons, up to the large coronene molecule in a complete active space of 24 pi electrons in 24 orbitals, requiring only modest computational resources.

physics.chem-ph↗

arXiv2015

An excited-state approach within full configuration interaction quantum Monte Carlo

We present a new approach to calculate excited states with the full configuration interaction quantum Monte Carlo (FCIQMC) method. The approach uses a Gram-Schmidt procedure, instantaneously applied to the stochastically evolving distributions of walkers, to orthogonalize higher energy states against lower energy ones. It can thus be used to study several of the lowest-energy states of a system within the same symmetry. This additional step is particularly simple and computationally inexpensive, requiring only a small change to the underlying FCIQMC algorithm. No trial wave functions or partitioning of the space is needed. The approach should allow excited states to be studied for systems similar to those accessible to the ground-state method, due to a comparable computational cost. As a first application we consider the carbon dimer in basis sets up to quadruple-zeta quality, and compare to existing results where available.

physics.comp-ph↗

arXiv2015

Multireference linearized Coupled Cluster theory for strongly correlated systems using Matrix Product States

We propose a multireference linearized coupled cluster theory using matrix product states (MPS-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration interaction singles and doubles (MRCISD), for a wide variety of electronic Hamiltonians. These range from first-row dimers at equilibrium and stretched geometries, to highly multireference systems such as the chromium dimer and lattice models such as periodic two-dimensional 1-band and 3-band Hubbard models. The MPS-LCC theory shows a speed up of several orders of magnitude over the usual DMRG algorithm while delivering energies in excellent agreement with converged DMRG calculations. Also, in all the benchmark calculations presented here MPS-LCC outperformed the commonly used multi-reference quantum chemistry methods in some cases giving energies in excess of an order of magnitude more accurate. As a size-extensive method that can treat large active spaces, MPS-LCC opens up the use of multireference quantum chemical techniques in strongly-correlated \emph{ab-initio} Hamiltonians, including two and three-dimensional solids.

physics.chem-ph↗

arXiv2015

Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in imaginary time independently from the first, and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality, and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation.

physics.comp-ph↗

arXiv2015

Krylov-projected quantum Monte Carlo

We present an approach to the calculation of arbitrary spectral, thermal and excited state properties within the full configuration interaction quantum Monte Carlo framework. This is achieved via an unbiased projection of the Hamiltonian eigenvalue problem into a space of stochastically sampled Krylov vectors, thus enabling the calculation of real-frequency spectral and thermal properties and avoiding explicit analytic continuation. We use this approach to calculate temperature-dependent properties and one- and two-body spectral functions for various Hubbard models, as well as isolated excited states in ab initio systems.

cond-mat.str-el↗

arXiv2015

Semi-stochastic full configuration interaction quantum Monte Carlo: developments and application

We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the Beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable.

physics.comp-ph↗

arXiv2014

Unbiased Reduced Density Matrices and Electronic Properties from Full Configuration Interaction Quantum Monte Carlo

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the Full Configuration Interaction Quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself), and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems.

physics.comp-ph↗

arXiv2013

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 Møller-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.

physics.comp-ph↗

arXiv2013

Linear-scaling and parallelizable algorithms for stochastic quantum chemistry

For many decades, quantum chemical method development has been dominated by algorithms which involve increasingly complex series of tensor contractions over one-electron orbital spaces. Procedures for their derivation and implementation have evolved to require the minimum amount of logic and rely heavily on computationally efficient library-based matrix algebra and optimized paging schemes. In this regard, the recent development of exact stochastic quantum chemical algorithms to reduce computational scaling and memory overhead requires a contrasting algorithmic philosophy, but one which when implemented efficiently can often achieve higher accuracy/cost ratios with small random errors. Additionally, they can exploit the continuing trend for massive parallelization which hinders the progress of deterministic high-level quantum chemical algorithms. In the Quantum Monte Carlo community, stochastic algorithms are ubiquitous but the discrete Fock space of quantum chemical methods is often unfamiliar, and the methods introduce new concepts required for algorithmic efficiency. In this paper, we explore these concepts and detail an algorithm used for Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which is implemented and available in MOLPRO and as a standalone code, and is designed for high-level parallelism and linear-scaling with walker number. Many of the algorithms are also in use in, or can be transferred to, other stochastic quantum chemical methods and implementations. We apply these algorithms to the strongly correlated Chromium dimer, to demonstrate their efficiency and parallelism.

physics.comp-ph↗

arXiv2012

Emergence of Critical Phenomena in Full Configuration Interaction Quantum Monte Carlo

There has been recent literature discussion on the origin and severity of the `sign problem' in full configuration interaction quantum Monte Carlo (FCIQMC) and its `initiator' adaptation (i-FCIQMC), methods of interest and potential because they allow for exact (FCI) ground-state solutions to be obtained often at a much reduced computational cost. In this study we aim to use a simple order parameter, describing the `sign structure' of the stochastic wavefunction representation, to empirically characterise the fundamentally different collective behaviour of the walker population in both methods.

physics.chem-ph↗

arXiv2012

An explicitly correlated approach to basis set incompleteness in Full Configuration Interaction Quantum Monte Carlo

By performing a stochastic dynamic in a space of Slater determinants, the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has been able to obtain energies which are essentially free from systematic error to the basis set correlation energy, within small and systematically improvable errorbars. However, the weakly exponential scaling with basis size makes converging the energy with respect to basis set costly and in larger systems, impossible. To ameliorate these basis set issues, here we use perturbation theory to couple the FCIQMC wave function to an explicitly correlated strongly orthogonal basis of geminals, following the [2]_{\textrm{R12}} approach of Valeev {\em et al.}. The required one- and two-particle density matrices are computed on-the-fly during the FCIQMC dynamic, using a sampling procedure which incurs relatively little additional computation expense. The F12 energy corrections are shown to converge rapidly as a function of sampling, both in imaginary time, and number of walkers. Our pilot calculations on the binding curve for carbon dimer, which exhibits strong correlation effects as well as substantial basis set dependence, demonstrate that the accuracy of the FCIQMC-F12 method surpasses that of all previous FCIQMC calculations, and that the F12 correction improves accuracy equivalent to increasing the quality of the one-electron basis by two cardinal numbers.

physics.comp-ph↗