Your browser doesn't support javascript.
loading
Show: 20 | 50 | 100
Results 1 - 20 de 32
Filter
Add more filters










Publication year range
1.
J Chem Phys ; 160(10)2024 Mar 14.
Article in English | MEDLINE | ID: mdl-38482870

ABSTRACT

We modify the reweighting factor of the projector used in diffusion Monte Carlo to reduce the time-step error of the total energy. Furthermore, we present a reweighting scheme that has the desirable feature that it is exactly size-consistent, i.e., the energy of a system containing widely separated fragments is the same as the sum of the energies of the individual fragments. The practical utility of the latter improvement is that it reduces the time-step error of the binding energies of some weakly interacting systems.

2.
J Am Chem Soc ; 144(35): 15932-15937, 2022 09 07.
Article in English | MEDLINE | ID: mdl-36001866

ABSTRACT

The complex electronic structure and unusual potential energy curve of the chromium dimer have fascinated scientists for decades, with agreement between theory and experiment so far elusive. Here, we present a new ab initio simulation of the potential energy curve and vibrational spectrum that significantly improves on all earlier estimates. Our data support a shift in earlier experimental assignments of a cluster of vibrational frequencies by one quantum number. The new vibrational assignment yields an experimentally derived potential energy curve in quantitative agreement with theory across all bond lengths and across all measured frequencies. By solving this long-standing problem, our results raise the possibility of quantitative quantum chemical modeling of transition metal clusters with spectroscopic accuracy.


Subject(s)
Chromium , Quantum Theory , Computer Simulation , Spectrum Analysis , Vibration
3.
J Chem Phys ; 155(20): 204104, 2021 Nov 28.
Article in English | MEDLINE | ID: mdl-34852493

ABSTRACT

The semistochastic heat-bath configuration interaction method is a selected configuration interaction plus perturbation theory method that has provided near-full configuration interaction (FCI) levels of accuracy for many systems with both single- and multi-reference character. However, obtaining accurate energies in the complete basis-set limit is hindered by the slow convergence of the FCI energy with respect to basis size. Here, we show that the recently developed basis-set correction method based on range-separated density functional theory can be used to significantly speed up basis-set convergence in SHCI calculations. In particular, we study two such schemes that differ in the functional used and apply them to transition metal atoms and monoxides to obtain total, ionization, and dissociation energies well converged to the complete-basis-set limit within chemical accuracy.

5.
J Chem Phys ; 154(21): 214110, 2021 Jun 07.
Article in English | MEDLINE | ID: mdl-34240977

ABSTRACT

We present a version of the T-moves approach for treating nonlocal pseudopotentials in diffusion Monte Carlo, which has much smaller time-step errors than the existing T-moves approaches, while at the same time preserving desirable features such as the upper-bound property for the energy. In addition, we modify the reweighting factor of the projector used in diffusion Monte Carlo to reduce the time-step error. The latter is applicable not only to pseudopotential calculations but also to all-electron calculations.

6.
J Chem Theory Comput ; 17(7): 4183-4194, 2021 Jul 13.
Article in English | MEDLINE | ID: mdl-34132530

ABSTRACT

We study several approaches to orbital optimization in selected configuration interaction (SCI) plus perturbation theory methods and test them on the ground and excited states of three molecules using the semistochastic heat-bath configuration interaction method. We discuss the ways in which the orbital optimization problem in SCI resembles and differs from that in complete active space self-consistent field. Starting from natural orbitals, these approaches divide into three classes of optimization methods according to how they treat coupling between configuration interaction coefficients and orbital parameters, namely uncoupled, fully coupled, and quasi-fully coupled methods. We demonstrate that taking the coupling into account is crucial for fast convergence and recommend two quasi-fully coupled methods for such applications: accelerated diagonal Newton and Broyden-Fletcher-Goldfarb-Shanno.

7.
J Chem Theory Comput ; 17(6): 3414-3425, 2021 Jun 08.
Article in English | MEDLINE | ID: mdl-34018739

ABSTRACT

We investigate the renormalized perturbative triples correction together with the externally corrected coupled-cluster singles and doubles (ecCCSD) method. We use the density matrix renormalization group (DMRG) and heat-bath CI (HCI) as external sources for the ecCCSD equations. The accuracy is assessed for the potential energy surfaces of H2O, N2, and F2. We find that the triples correction significantly improves upon ecCCSD, and we do not see any instability of the renormalized triples with respect to dissociation. We explore how to balance the cost of computing the external source amplitudes against the accuracy of the subsequent CC calculation. In this context, we find that very approximate wave functions (and their large amplitudes) serve as an efficient and accurate external source. Finally, we characterize the domain of correlation treatable using the ecCCSD and renormalized triples combination studied in this work via a well-known wave function diagnostic.

8.
J Phys Chem Lett ; 11(20): 8922-8929, 2020 Oct 15.
Article in English | MEDLINE | ID: mdl-33022176

ABSTRACT

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground-state energy of the benzene molecule in a standard correlation-consistent basis set of double-ζ quality. As a broad international endeavor, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around -863 mEH. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 mEH), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

9.
J Chem Phys ; 153(12): 124117, 2020 Sep 28.
Article in English | MEDLINE | ID: mdl-33003731

ABSTRACT

The recently developed semistochastic heat-bath configuration interaction (SHCI) method is a systematically improvable selected configuration interaction plus perturbation theory method capable of giving essentially exact energies for larger systems than is possible with other such methods. We compute SHCI atomization energies for 55 molecules that have been used as a test set in prior studies because their atomization energies are known from experiment. Basis sets from cc-pVDZ to cc-pV5Z are used, totaling up to 500 orbitals and a Hilbert space of 1032 Slater determinants for the largest molecules. For each basis, an extrapolated energy well within chemical accuracy (1 kcal/mol or 1.6 mHa/mol) of the exact energy for that basis is computed using only a tiny fraction of the entire Hilbert space. We also use our almost exact energies to benchmark energies from the coupled cluster method with single, double, and perturbative triple excitations. The energies are extrapolated to the complete basis set limit and compared to the experimental atomization energies. The extrapolations are done both without and with a basis-set correction based on density-functional theory. The mean absolute deviations from experiment for these extrapolations are 0.46 kcal/mol and 0.51 kcal/mol, respectively. Orbital optimization methods used to obtain improved convergence of the SHCI energies are also discussed.

10.
J Chem Phys ; 150(2): 024302, 2019 Jan 14.
Article in English | MEDLINE | ID: mdl-30646701

ABSTRACT

We report that a recent active space model of the nitrogenase FeMo cofactor, proposed in the context of simulations on quantum computers, is not representative of the electronic structure of the FeMo cofactor ground-state. A more representative model does not affect much certain resource estimates for a quantum computer such as the cost of a Trotter step, while strongly affecting others such as the cost of adiabatic state preparation. Thus, conclusions should not be drawn from the complexity of quantum or classical simulations of the electronic structure of this system in this active space. We provide a different model active space for the FeMo cofactor that contains the basic open-shell qualitative character, which may be useful as a benchmark system for making resource estimates for classical and quantum computers.

11.
J Chem Phys ; 149(21): 214110, 2018 Dec 07.
Article in English | MEDLINE | ID: mdl-30525735

ABSTRACT

This paper presents in detail our fast semistochastic heat-bath configuration interaction (SHCI) method for solving the many-body Schrödinger equation. We identify and eliminate computational bottlenecks in both the variational and perturbative steps of the SHCI algorithm. We also describe the parallelization and the key data structures in our implementation, such as the distributed hash table. The improved SHCI algorithm enables us to include in our variational wavefunction two orders of magnitude more determinants than has been reported previously with other selected configuration interaction methods. We use our algorithm to calculate an accurate benchmark energy for the chromium dimer with the X2C relativistic Hamiltonian in the cc-pVDZ-DK basis, correlating 28 electrons in 76 spatial orbitals. Our largest calculation uses two billion Slater determinants in the variational space and semistochastically includes perturbative contributions from at least trillions of additional determinants with better than 10-5 Ha statistical uncertainty.

12.
J Phys Chem A ; 122(10): 2714-2722, 2018 Mar 15.
Article in English | MEDLINE | ID: mdl-29473750

ABSTRACT

The electronically excited states of methylene (CH2), ethylene (C2H4), butadiene (C4H6), hexatriene (C6H8), and ozone (O3) have long proven challenging due to their complex mixtures of static and dynamic correlations. The semistochastic heat-bath configuration interaction (SHCI) algorithm, which efficiently and systematically approaches the full configuration interaction (FCI) limit, is used to provide close approximations to the FCI energies in these systems. This article presents the largest FCI-level calculation to date on hexatriene, using a polarized double-ζ basis (ANO-L-pVDZ), which gives rise to a Hilbert space containing more than 1038 determinants. These calculations give vertical excitation energies of 5.58 and 5.59 eV, respectively, for the 21Ag and 11Bu states, showing that they are nearly degenerate. The same excitation energies in butadiene/ANO-L-pVDZ were found to be 6.58 and 6.45 eV. In addition to these benchmarks, our calculations strongly support the presence of a previously hypothesized ring-minimum species of ozone that lies 1.3 eV higher than the open-ring-minimum energy structure and is separated from it by a barrier of 1.11 eV.

13.
J Chem Phys ; 147(16): 164111, 2017 Oct 28.
Article in English | MEDLINE | ID: mdl-29096501

ABSTRACT

We extend our recently developed heat-bath configuration interaction (HCI) algorithm, and our semistochastic algorithm for performing multireference perturbation theory, to calculate excited-state wavefunctions and energies. We employ time-reversal symmetry, which reduces the memory requirements by more than a factor of two. An extrapolation technique is introduced to reliably extrapolate HCI energies to the full CI limit. The resulting algorithm is used to compute fourteen low-lying potential energy surfaces of the carbon dimer using the cc-pV5Z basis set, with an estimated error in energy of 30-50 µHa compared to full CI. The excitation energies obtained using our algorithm have a mean absolute deviation of 0.02 eV compared to experimental values.

14.
J Chem Theory Comput ; 13(4): 1595-1604, 2017 Apr 11.
Article in English | MEDLINE | ID: mdl-28263594

ABSTRACT

We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 2016, 12, 3674], 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 wave function, 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-ζ 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 s, 37 s, and 56 min on 1, 1, and 4 nodes, respectively.

15.
J Chem Theory Comput ; 12(8): 3674-80, 2016 Aug 09.
Article in English | MEDLINE | ID: mdl-27428771

ABSTRACT

We introduce a new selected configuration interaction plus perturbation theory algorithm that is based on a deterministic analog of our recent efficient heat-bath sampling algorithm. This Heat-bath Configuration Interaction (HCI) algorithm makes use of two parameters that control the trade-off between speed and accuracy, one which controls the selection of determinants to add to a variational wave function and one which controls the selection of determinants used to compute the perturbative correction to the variational energy. We show that HCI provides an accurate treatment of both static and dynamic correlation by computing the potential energy curve of the multireference carbon dimer in the cc-pVDZ basis. We then demonstrate the speed and accuracy of HCI by recovering the full configuration interaction energy of both the carbon dimer in the cc-pVTZ basis and the strongly correlated chromium dimer in the Ahlrichs VDZ basis, correlating all electrons, to an accuracy of better than 1 mHa, in just a few minutes on a single core. These systems have full variational spaces of 3 × 10(14) and 2 × 10(22) determinants, respectively.

16.
J Chem Theory Comput ; 12(4): 1561-71, 2016 Apr 12.
Article in English | MEDLINE | ID: mdl-26959242

ABSTRACT

We introduce an algorithm for sampling many-body quantum states in Fock space. The algorithm efficiently samples states with probability approximately proportional to an arbitrary function of the second-quantized Hamiltonian matrix element connecting the sampled state to the current state. We apply the new sampling algorithm to the recently developed semistochastic full configuration interaction quantum Monte Carlo (S-FCIQMC) method, a semistochastic implementation of the power method for projecting out the ground state energy in a basis of Slater determinants. Our new sampling method requires modest additional computational time and memory compared to uniform sampling but results in newly spawned weights that are approximately of the same magnitude, thereby greatly improving the efficiency of projection. A comparison in efficiency between our sampling algorithm and uniform sampling is performed on the all-electron nitrogen dimer at equilibrium in Dunning's cc-pVXZ basis sets with X ∈ {D, T, Q, 5}, demonstrating a large gain in efficiency that increases with basis set size. In addition, a comparison in efficiency is performed on three all-electron first-row dimers, B2, N2, and F2, in a cc-pVQZ basis, demonstrating that the gain in efficiency compared to uniform sampling also increases dramatically with the number of electrons.

17.
J Chem Phys ; 143(16): 164105, 2015 Oct 28.
Article in English | MEDLINE | ID: mdl-26520496

ABSTRACT

Variational Monte Carlo and various projector Monte Carlo (PMC) methods are presented in a unified manner. Similarities and differences between the methods and choices made in designing the methods are discussed. Both methods where the Monte Carlo walk is performed in a discrete space and methods where it is performed in a continuous space are considered. It is pointed out that the usual prescription for importance sampling may not be advantageous depending on the particular quantum Monte Carlo method used and the observables of interest, so alternate prescriptions are presented. The nature of the sign problem is discussed for various versions of PMC methods. A prescription for an exact PMC method in real space, i.e., a method that does not make a fixed-node or similar approximation and does not have a finite basis error, is presented. This method is likely to be practical for systems with a small number of electrons. Approximate PMC methods that are applicable to larger systems and go beyond the fixed-node approximation are also discussed.

18.
J Chem Phys ; 140(18): 18A532, 2014 May 14.
Article in English | MEDLINE | ID: mdl-24832340

ABSTRACT

Anions and radicals are important for many applications including environmental chemistry, semiconductors, and charge transfer, but are poorly described by the available approximate energy density functionals. Here we test an approximate exchange-correlation functional based on the exact strong-coupling limit of the Hohenberg-Kohn functional on the prototypical case of the He isoelectronic series with varying nuclear charge Z < 2, which includes weakly bound negative ions and a quantum phase transition at a critical value of Z, representing a big challenge for density functional theory. We use accurate wavefunction calculations to validate our results, comparing energies and Kohn-Sham potentials, thus also providing useful reference data close to and at the quantum phase transition. We show that our functional is able to bind H(-) and to capture in general the physics of loosely bound anions, with a tendency to strongly overbind that can be proven mathematically. We also include corrections based on the uniform electron gas which improve the results.

19.
J Chem Phys ; 140(10): 104112, 2014 Mar 14.
Article in English | MEDLINE | ID: mdl-24628157

ABSTRACT

We combine explicit correlation via the canonical transcorrelation approach with the density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods to compute a near-exact beryllium dimer curve, without the use of composite methods. In particular, our direct density matrix renormalization group calculations produce a well-depth of D(e) = 931.2 cm(-1) which agrees very well with recent experimentally derived estimates D(e) = 929.7±2 cm(-1) [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)] and D(e) = 934.6 cm(-1) [K. Patkowski, V. Spirko, and K. Szalewicz, Science 326, 1382 (2009)], as well the best composite theoretical estimates, D(e) = 938±15 cm(-1) [K. Patkowski, R. Podeszwa, and K. Szalewicz, J. Phys. Chem. A 111, 12822 (2007)] and D(e) = 935.1±10 cm(-1) [J. Koput, Phys. Chem. Chem. Phys. 13, 20311 (2011)]. Our results suggest possible inaccuracies in the functional form of the potential used at shorter bond lengths to fit the experimental data [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)]. With the density matrix renormalization group we also compute near-exact vertical excitation energies at the equilibrium geometry. These provide non-trivial benchmarks for quantum chemical methods for excited states, and illustrate the surprisingly large error that remains for 1 ¹Σ(g)⁻ state with approximate multi-reference configuration interaction and equation-of-motion coupled cluster methods. Overall, we demonstrate that explicitly correlated density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods allow us to fully converge to the basis set and correlation limit of the non-relativistic Schrödinger equation in small molecules.

20.
Phys Rev Lett ; 110(24): 246802, 2013 Jun 14.
Article in English | MEDLINE | ID: mdl-25165952

ABSTRACT

We study the quantum phase transition of interacting electrons in quantum wires from a one-dimensional (1D) linear configuration to a quasi-1D zigzag arrangement using quantum Monte Carlo methods. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal, then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase, and, finally, the electrons form a disordered liquidlike phase. We show that the linear to zigzag phase transition is not destroyed by the strong quantum fluctuations present in narrow wires; it has characteristics which are qualitatively different from the classical transition.

SELECTION OF CITATIONS
SEARCH DETAIL
...