Showing papers on "Coupled cluster published in 2017"

Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz

Abstract: The variational quantum eigensolver (VQE) algorithm combines the ability of quantum computers to efficiently compute expectation values with a classical optimization routine in order to approximate ground state energies of quantum systems. In this paper, we study the application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz. We introduce new strategies to reduce the circuit depth for the implementation of UCC and improve the optimization of the wavefunction based on efficient classical approximations of the cluster amplitudes. Additionally, we propose an analytical method to compute the energy gradient that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients. We illustrate our methodology with numerical simulations for a system of four hydrogen atoms that exhibit strong correlation and show that the circuit depth of VQE using a UCC ansatz can be reduced without introducing significant loss of accuracy in the final wavefunctions and energies.

A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory.

Abstract: The Coupled-Cluster expansion, truncated after single and double excitations (CCSD), provides accurate and reliable molecular electronic wave functions and energies for many molecular systems around their equilibrium geometries. However, the high computational cost, which is well-known to scale as O(N6) with system size N, has limited its practical application to small systems consisting of not more than approximately 20-30 atoms. To overcome these limitations, low-order scaling approximations to CCSD have been intensively investigated over the past few years. In our previous work, we have shown that by combining the pair natural orbital (PNO) approach and the concept of orbital domains it is possible to achieve fully linear scaling CC implementations (DLPNO-CCSD and DLPNO-CCSD(T)) that recover around 99.9% of the total correlation energy [C. Riplinger et al., J. Chem. Phys. 144, 024109 (2016)]. The production level implementations of the DLPNO-CCSD and DLPNO-CCSD(T) methods were shown to be applicable to realistic systems composed of a few hundred atoms in a routine, black-box fashion on relatively modest hardware. In 2011, a reduced-scaling CCSD approach for high-spin open-shell unrestricted Hartree-Fock reference wave functions was proposed (UHF-LPNO-CCSD) [A. Hansen et al., J. Chem. Phys. 135, 214102 (2011)]. After a few years of experience with this method, a few shortcomings of UHF-LPNO-CCSD were noticed that required a redesign of the method, which is the subject of this paper. To this end, we employ the high-spin open-shell variant of the N-electron valence perturbation theory formalism to define the initial guess wave function, and consequently also the open-shell PNOs. The new PNO ansatz properly converges to the closed-shell limit since all truncations and approximations have been made in strict analogy to the closed-shell case. Furthermore, given the fact that the formalism uses a single set of orbitals, only a single PNO integral transformation is necessary, which offers large computational savings. We show that, with the default PNO truncation parameters, approximately 99.9% of the total CCSD correlation energy is recovered for open-shell species, which is comparable to the performance of the method for closed-shells. UHF-DLPNO-CCSD shows a linear scaling behavior for closed-shell systems, while linear to quadratic scaling is obtained for open-shell systems. The largest systems we have considered contain more than 500 atoms and feature more than 10 000 basis functions with a triple-ζ quality basis set.

Gaussian-Based Coupled-Cluster Theory for the Ground-State and Band Structure of Solids.

Abstract: We present the results of Gaussian-based ground-state and excited-state equation-of-motion coupled-cluster theory with single and double excitations for three-dimensional solids. We focus on diamond and silicon, which are paradigmatic covalent semiconductors. In addition to ground-state properties (the lattice constant, bulk modulus, and cohesive energy), we compute the quasiparticle band structure and band gap. We sample the Brillouin zone with up to 64 k-points using norm-conserving pseudopotentials and polarized double- and triple-ζ basis sets, leading to canonical coupled-cluster calculations with as many as 256 electrons in 2176 orbitals.

Scalable Electron Correlation Methods. 3. Efficient and Accurate Parallel Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD)

Abstract: A well-parallelized local singles and doubles coupled-cluster (LCCSD) method using pair natural virtual orbitals (PNOs) is presented. The PNOs are constructed using large domains of projected atomic orbitals (PAOs) and orbital specific virtual orbitals (OSVs). We introduce a hierarchy of close, weak, and distant pairs, based on pair energies evaluated by local Moller–Plesset perturbation theory (LMP2). In contrast to most previous implementations of LCCSD methods, the close and weak pairs are not approximated by LMP2 but treated by higher-order methods. This leads to greatly improved accuracy for large systems, in particular when long-range dispersion interactions are important. Close pair amplitudes are optimized using approximate LCCSD equations, in which slowly decaying terms that mutually cancel at long-range are neglected. For weak pairs, the same approximations are used, but in addition, the nonlinear terms are neglected (coupled electron pair approximation). Distant pairs are treated by spin-compon...

SparseMaps—A systematic infrastructure for reduced scaling electronic structure methods. V. Linear scaling explicitly correlated coupled-cluster method with pair natural orbitals

Abstract: In this work, we present a linear scaling formulation of the coupled-cluster singles and doubles with perturbative inclusion of triples (CCSD(T)) and explicitly correlated geminals. The linear scaling implementation of all post-mean-field steps utilizes the SparseMaps formalism [P. Pinski et al., J. Chem. Phys. 143, 034108 (2015)]. Even for conservative truncation levels, the method rapidly reaches near-linear complexity in realistic basis sets, e.g., an effective scaling exponent of 1.49 was obtained for n-alkanes with up to 200 carbon atoms in a def2-TZVP basis set. The robustness of the method is benchmarked against the massively parallel implementation of the conventional explicitly correlated coupled-cluster for a 20-water cluster; the total dissociation energy of the cluster (∼186 kcal/mol) is affected by the reduced scaling approximations by only ∼0.4 kcal/mol. The reduced scaling explicitly correlated CCSD(T) method is used to examine the binding energies of several systems in the L7 benchmark data set of noncovalent interactions.

Efficient DLPNO–CCSD(T)-Based Estimation of Formation Enthalpies for C-, H-, O-, and N-Containing Closed-Shell Compounds Validated Against Critically Evaluated Experimental Data

Abstract: An accurate and cost-efficient methodology for the estimation of the enthalpies of formation for closed-shell compounds composed of C, H, O, and N atoms is presented and validated against critically evaluated experimental data The computational efficiency is achieved through the use of the resolution-of-identity (RI) and domain-based local pair-natural orbital coupled cluster (DLPNO–CCSD(T)) approximations, which results in a drastic reduction in both the computational cost and the number of necessary steps for a composite quantum chemical method The expanded uncertainty for the proposed methodology evaluated using a data set of 45 thoroughly vetted experimental values for molecules containing up to 12 heavy atoms is about 3 kJ·mol–1, competitive with those of typical calorimetric measurements For the compounds within the stated scope, the methodology is shown to be superior to a representative, more general, and widely used composite quantum chemical method, G4

Prediction of Bond Dissociation Energies/Heats of Formation for Diatomic Transition Metal Compounds: CCSD(T) Works.

Abstract: It was recently reported (J. Chem. Theory Comput. 2015, 11, 2036−2052) that the coupled cluster singles and doubles with perturbative triples method, CCSD(T), should not be used as a benchmark tool for the prediction of dissociation energies (heats of formation) for the first row transition metal diatomics based on a comparison with the experimental thermodynamic values for a set of 20 diatomics. In the present work the bond dissociation energies as well as the heats of formation for those diatomics have been calculated by the Feller–Peterson–Dixon approach at the CCSD(T)/complete basis set (CBS) level of theory including scalar relativistic corrections and correlation of the outer shell of core electrons in addition to the valence electrons. Revised experimental values for the hydrides are presented that are based on new heterolytic R–H bond dissociation energies, which are needed for analysis of the mass spectrometry experiments. The agreement between the calculated bond dissociation energies and the re...

Converging High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions.

Abstract: We propose a new approach to the determination of accurate electronic energies that are equivalent to the results of high-level coupled-cluster (CC) calculations. The approach is based on merging the CC(P;Q) formalism, which corrects energies obtained with an arbitrary truncation in the cluster operator, with the stochastic configuration interaction and CC ideas. The advantages of the proposed methodology are illustrated by molecular examples, where the goal is to recover the energetics obtained in the CC calculations with a full treatment of singly, doubly, and triply excited clusters.

Simulation of Near-Edge X-ray Absorption Fine Structure with Time-Dependent Equation-of-Motion Coupled-Cluster Theory.

Abstract: An explicitly time-dependent (TD) approach to equation-of-motion (EOM) coupled-cluster theory with single and double excitations (CCSD) is implemented for simulating near-edge X-ray absorption fine structure in molecular systems. The TD-EOM-CCSD absorption line shape function is given by the Fourier transform of the CCSD dipole autocorrelation function. We represent this transform by its Pade approximant, which provides converged spectra in much shorter simulation times than are required by the Fourier form. The result is a powerful framework for the blackbox simulation of broadband absorption spectra. K-edge X-ray absorption spectra for carbon, nitrogen, and oxygen in several small molecules are obtained from the real part of the absorption line shape function and are compared with experiment. The computed and experimentally obtained spectra are in good agreement; the mean unsigned error in the predicted peak positions is only 1.2 eV. We also explore the spectral signatures of protonation in these molecules.

Relativistic Coupled Cluster Calculations with Variational Quantum Electrodynamics Resolve the Discrepancy between Experiment and Theory Concerning the Electron Affinity and Ionization Potential of Gold.

Abstract: The first ionization potential (IP) and electron affinity (EA) of the gold atom have been determined to an unprecedented accuracy using relativistic coupled cluster calculations up to the pentuple excitation level including the Breit and QED contributions. We reach meV accuracy (with respect to the experimental values) by carefully accounting for all individual contributions beyond the standard relativistic coupled cluster approach. Thus, we are able to resolve the long-standing discrepancy between experimental and theoretical IP and EA of gold.

Bond Dissociation Energies for Diatomic Molecules Containing 3d Transition Metals: Benchmark Scalar-Relativistic Coupled-Cluster Calculations for 20 Molecules.

Abstract: Benchmark scalar-relativistic coupled-cluster calculations for dissociation energies of the 20 diatomic molecules containing 3d transition metals in the 3dMLBE20 database (J. Chem. Theory Comput. 2015, 11, 2036) are reported. Electron correlation and basis set effects are systematically studied. The agreement between theory and experiment is in general satisfactory. For a subset of 16 molecules, the standard deviation between computational and experimental values is 9 kJ/mol with the maximum deviation being 15 kJ/mol. The discrepancies between theory and experiment remain substantial (more than 20 kJ/mol) for VH, CrH, CoH, and FeH. To explore the source of the latter discrepancies, the analysis used to determine the experimental dissociation energies for VH and CrH is revisited. It is shown that, if improved values are used for the heterolytic C–H dissociation energies of di- and trimethylamine involved in the experimental determination, the experimental values for the dissociation energies of VH and CrH ...

Time-dependent optimized coupled-cluster method for multielectron dynamics

Abstract: Time-dependent coupled-cluster method with time-varying orbital functions, called time-dependent optimized coupled- cluster (TD-OCC) method, is formulated for multielectron dynamics in an intense laser field. We have successfully derived equations of motion for CC amplitudes and orthonormal orbital functions based on the real action functional, and implemented the method including double excitations (TD-OCCD) and double and triple excitations (TD-OCCDT) within the optimized active orbitals. The present method is size extensive and gauge invariant, a polynomial cost-scaling alternative to the time-dependent multiconfiguration self-consistent-field method. The first application of the TD-OCC method to intense-laser driven correlated electron dynamics in Ar atom is reported.

Low rank factorization of the Coulomb integrals for periodic coupled cluster theory.

Abstract: We study a tensor hypercontraction decomposition of the Coulomb integrals of periodic systems where the integrals are factorized into a contraction of six matrices of which only two are distinct. We find that the Coulomb integrals can be well approximated in this form already with small matrices compared to the number of real space grid points. The cost of computing the matrices scales as O(N4) using a regularized form of the alternating least squares algorithm. The studied factorization of the Coulomb integrals can be exploited to reduce the scaling of the computational cost of expensive tensor contractions appearing in the amplitude equations of coupled cluster methods with respect to system size. We apply the developed methodologies to calculate the adsorption energy of a single water molecule on a hexagonal boron nitride monolayer in a plane wave basis set and periodic boundary conditions.

Scalable Electron Correlation Methods. 4. Parallel Explicitly Correlated Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD-F12)

Abstract: We present an efficient explicitly correlated pair natural orbital local coupled cluster (PNO-LCCSD-F12) method. The method is an extension of our previously reported PNO-LCCSD approach (Schwilk et al., J. Chem. Theory Comput. DOI: 10.1021/acs.jctc.7b00554). Near linear scaling with the size of molecule is achieved by using pair, domain, and projection approximations, local density fitting, local resolution of the identity, and by exploiting the sparsity of the local molecular orbitals as well as of the projected atomic orbitals. The effect of the various domain approximations is tested for a wide range of chemical reactions and intermolecular interactions. In accordance with previous findings it is demonstrated that the F12 terms significantly reduce the domain errors. The convergence of the reaction and interaction energies with respect to the parameters that determine the domain sizes and pair approximations is extensively tested. The results obtained with our default thresholds agree within a few tent...

Basis set convergence of the binding energies of strongly hydrogen-bonded atmospheric clusters

Abstract: We investigate the basis set convergence of second order Moller Plesset perturbation theory for the binding energies of 11 strongly hydrogen-bonded clusters relevant to the atmosphere. The binding energies are calculated both as the uncorrected (UC) value, as well as by employing the counterpoise (CP) and the Same Number Of Optimized Parameters (SNOOP) correction schemes, with and without explicit correlation (F12). We find that the use of the F12 corrections is of utter importance for obtaining converged binding energies. Without F12 corrections at least a quadruple-ζ basis set is generally required to yield errors below 1 kcal mol−1 compared to the complete basis set (CBS) limit. Using coupled cluster methods we obtain a best estimate of the CCSD(T) CBS limit of the binding energies of the considered clusters and compare it with approximate DLPNO-CCSD(T) and DFT methods. We identify a pragmatic approach, relying solely on a series of double-ζ basis set calculations, for obtaining results in remarkably good agreement with our CBS estimate.

Coupled-Cluster Valence-Bond Singles and Doubles for Strongly Correlated Systems: Block-Tensor Based Implementation and Application to Oligoacenes.

Abstract: We demonstrate a block-tensor based implementation of coupled-cluster valence-bond singles and doubles (CCVB-SD) [Small, D. W.; Head-Gordon M. J. Chem. Phys. 2012, 137, 114103] which is a simple modification to restricted CCSD (RCCSD) that provides a qualitatively correct description of valence correlations even in strongly correlated systems. We derive the Λ-equation of CCVB-SD and the corresponding unrelaxed density matrices. The resulting production-level implementation is applied to oligoacenes, correlating up to 318 electrons in 318 orbitals. CCVB-SD shows a qualitative agreement with exact methods for short acenes and reaches the bulk limit of oligoacenes in terms of natural orbital occupation numbers, whereas RCCSD shows nonvariational behavior even for relatively short acenes. A significant reduction in polyradicaloid character is found when correlating all valence electrons instead of only the π-electrons.

Projected coupled cluster theory.

Abstract: Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system or has to artificially break certain symmetries. On the other hand, projected Hartree-Fock theory captures the essential physics of many kinds of strong correlations via symmetry breaking and restoration. In this work, we combine and try to retain the merits of these two methods by applying symmetry projection to broken symmetry coupled cluster wave functions. The non-orthogonal nature of states resulting from the application of symmetry projection operators furnishes particle-hole excitations to all orders, thus creating an obstacle for the exact evaluation of overlaps. Here we provide a solution via a disentanglement framework theory that can be approximated rigorously and systematically. Results of projected coupled cluster theory are presented for molecules and the Hubbard model, showing that spin projection significantly improves unrestricted coupled cluster theory while restoring good quantum numbers. The energy of projected coupled cluster theory reduces to the unprojected one in the thermodynamic limit, albeit at a much slower rate than projected Hartree-Fock.

Diamines Can Initiate New Particle Formation in the Atmosphere.

Abstract: Recent experimental evidence suggests that diamines can enhance atmospheric new particle formation more efficiently compared to monoamines such as dimethylamine. Here we investigate the molecular interactions between sulfuric acid (sa) and the diamine putrescine (put) using computational methods. The molecular structure of up to four sulfuric acid molecules and up to four putrescine molecules were obtained at the ωB97X-D/6-31++G(d,p) level of theory. We utilized a domain local pair natural orbital coupled cluster method (DLPNO-CCSD(T)/aug-cc-pVTZ) to obtain highly accurate binding energies of the clusters. We find that the (sa)1–4(put)1–4 clusters show more ionic character than clusters consisting of sulfuric acid and dimethylamine (dma) by readily forming several sulfate ions in the cluster. To estimate the stability of the clusters, we calculate the evaporation rates and compare them to ESI-APi-TOF measurements. Using the atmospheric cluster dynamics code (ACDC), we simulate and compare the new particle...

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory.

Abstract: We present two efficient and intruder-free methods for treating dynamic correlation on top of general multiconfiguration 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 multireference linearized coupled cluster method (MRLCC) [Sharma, S.; Alavi, A. J. Chem. Phys. 2015, 143, 102815] 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 ...

Correlation consistent basis sets for actinides. II. The atoms Ac and Np–Lr

Abstract: New correlation consistent basis sets optimized using the all-electron third-order Douglas-Kroll-Hess (DKH3) scalar relativistic Hamiltonian are reported for the actinide elements Ac and Np through Lr. These complete the series of sets reported previously for Th-U [K. A. Peterson, J. Chem. Phys. 142, 074105 (2015); M. Vasiliu et al., J. Phys. Chem. A 119, 11422 (2015)]. The new sets range in size from double- to quadruple-zeta and encompass both those optimized for valence (6s6p5f7s6d) and outer-core electron correlations (valence + 5s5p5d). The final sets have been contracted for both the DKH3 and eXact 2-component (X2C) Hamiltonians, yielding cc-pVnZ-DK3/cc-pVnZ-X2C sets for valence correlation and cc-pwCVnZ-DK3/cc-pwCVnZ-X2C sets for outer-core correlation (n = D, T, Q in each case). In order to test the effectiveness of the new basis sets, both atomic and molecular benchmark calculations have been carried out. In the first case, the first three atomic ionization potentials (IPs) of all the actinide elements Ac-Lr have been calculated using the Feller-Peterson-Dixon (FPD) composite approach, primarily with the multireference configuration interaction (MRCI) method. Excellent convergence towards the respective complete basis set (CBS) limits is achieved with the new sets, leading to good agreement with experiment, where these exist, after accurately accounting for spin-orbit effects using the 4-component Dirac-Hartree-Fock method. For a molecular test, the IP and atomization energy (AE) of PuO2 have been calculated also using the FPD method but using a coupled cluster approach with spin-orbit coupling accounted for using the 4-component MRCI. The present calculations yield an IP0 for PuO2 of 159.8 kcal/mol, which is in excellent agreement with the experimental electron transfer bracketing value of 162 ± 3 kcal/mol. Likewise, the calculated 0 K AE of 305.6 kcal/mol is in very good agreement with the currently accepted experimental value of 303.1 ± 5 kcal/mol. The ground state of PuO2 is predicted to be the Σ0g+5 state.

Tensor-structured coupled cluster theory

Abstract: We derive and implement a new way of solving coupled cluster equations with lower computational scaling. Our method is based on the decomposition of both amplitudes and two electron integrals, using a combination of tensor hypercontraction and canonical polyadic decomposition. While the original theory scales as O(N6) with respect to the number of basis functions, we demonstrate numerically that we achieve sub-millihartree difference from the original theory with O(N4) scaling. This is accomplished by solving directly for the factors that decompose the cluster operator. The proposed scheme is quite general and can be easily extended to other many-body methods.

Automatic active space selection for the similarity transformed equations of motion coupled cluster method.

Abstract: An efficient scheme for the automatic selection of an active space for similarity transformed equations of motion (STEOM) coupled cluster method is proposed. It relies on state averaged configuration interaction singles (CIS) natural orbitals and makes it possible to use STEOM as a black box method. The performance of the new scheme is tested for singlet and triplet valence, charge transfer, and Rydberg excited states.

A Comparison of Quantum and Molecular Mechanical Methods to Estimate Strain Energy in Druglike Fragments

Abstract: Reducing internal strain energy in small molecules is critical for designing potent drugs. Quantum mechanical (QM) and molecular mechanical (MM) methods are often used to estimate these energies. In an effort to determine which methods offer an optimal balance in accuracy and performance, we have carried out torsion scan analyses on 62 fragments. We compared nine QM and four MM methods to reference energies calculated at a higher level of theory: CCSD(T)/CBS single point energies (coupled cluster with single, double, and perturbative triple excitations at the complete basis set limit) calculated on optimized geometries using MP2/6-311+G**. The results show that both the more recent MP2.X perturbation method as well as MP2/CBS perform quite well. In addition, combining a Hartree–Fock geometry optimization with a MP2/CBS single point energy calculation offers a fast and accurate compromise when dispersion is not a key energy component. Among MM methods, the OPLS3 force field accurately reproduces CCSD(T)/CB...

Symmetry broken and restored coupled-cluster theory: II. Global gauge symmetry and particle number

Abstract: We have recently extended many-body perturbation theory and coupled-cluster theory performed on top of a Slater determinant breaking rotational symmetry to allow for the restoration of the angular momentum at any truncation order (T. Duguet, $\it J. Phys. G: Nucl. Part. Phys.$ 42, 025107 (2015). Following a similar route, we presently extend Bogoliubov many-body perturbation theory and Bogoliubov coupled cluster theory performed on top of a Bogoliubov reference state breaking global gauge symmetry to allow for the restoration of the particle number at any truncation order. Eventually, formalisms can be merged to handle $SU(2)$ and $U(1)$ symmetries at the same time. Several further extensions of the newly proposed many-body formalisms can be foreseen in the mid-term future. The long-term goal relates to the $ab\ initio$ description of near-degenerate finite quantum systems with an open-shell character.

Elucidating the Limiting Steps in Sulfuric Acid-Base New Particle Formation

Abstract: The molecular interactions between sulfuric acid (sa) and methylamine (ma) are investigated using computational methods. The molecular structures and vibrational frequencies of (sa)a(ma)b clusters, with a, b ≤ 4, were obtained with the ωB97X-D functional using a 6-31++G(d,p) basis set. The single-point energies were corrected using the domain-based local pair natural orbital coupled cluster method—DLPNO–CCSD(T)—with an aug-cc-pVTZ basis set. The calculated Gibbs free energies (ΔG) of the clusters are used to calculate the evaporation rates of the (sa)a(ma)b cluster system and compare them to the corresponding ammonia clusters. With the atmospheric cluster dynamics code (ACDC), the new particle formation rates of the (sa)a(ma)b clusters were simulated and compared to the (sa)a(dma)b cluster system. It is found that methylamine is not capable of explaining observed new particle formation event in the ambient atmosphere. Looking into the calculated Gibbs free energy profiles it is found that the limiting ste...

Time-Step Targeting Time-Dependent and Dynamical Density Matrix Renormalization Group Algorithms with ab Initio Hamiltonians

Abstract: We study the dynamical density matrix renormalization group (DDMRG) and time-dependent density matrix renormalization group (td-DMRG) algorithms in the ab initio context to compute dynamical correlation functions of correlated systems. We analyze the strengths and weaknesses of the two methods in small model problems and propose two simple improved formulations, DDMRG++ and td-DMRG++, that give increased accuracy at the same bond dimension at a nominal increase in cost. We apply DDMRG++ to obtain the oxygen core-excitation energy in the water molecule in a quadruple-zeta quality basis, which allows us to estimate the remaining correlation error in existing coupled cluster results. Further, we use DDMRG++ to compute the local density of states and gaps and td-DMRG++ to compute the complex polarization function, in linear hydrogen chains with up to 50 H atoms, to study metallicity and delocalization as a function of bond length.

Shape and energy consistent pseudopotentials for correlated electron systems

Abstract: A method is developed for generating pseudopotentials for use in correlated-electron calculations. The paradigms of shape and energy consistency are combined and defined in terms of correlated-electron wave-functions. The resulting energy consistent correlated electron pseudopotentials (eCEPPs) are constructed for H, Li–F, Sc–Fe, and Cu. Their accuracy is quantified by comparing the relaxed molecular geometries and dissociation energies which they provide with all electron results, with all quantities evaluated using coupled cluster singles, doubles, and triples calculations. Errors inherent in the pseudopotentials are also compared with those arising from a number of approximations commonly used with pseudopotentials. The eCEPPs provide a significant improvement in optimised geometries and dissociation energies for small molecules, with errors for the latter being an order-of-magnitude smaller than for Hartree-Fock-based pseudopotentials available in the literature. Gaussian basis sets are optimised for ...

Accurate Excited-State Geometries: A CASPT2 and Coupled-Cluster Reference Database for Small Molecules

Abstract: We present an investigation of the excited-state structural parameters determined for a large set of small compounds with the dual goals of defining reference values for further works and assessing the quality of the geometries obtained with relatively cheap computational approaches. In the first stage, we compare the excited-state geometries obtained with ADC(2), CC2, CCSD, CCSDR(3), CC3, and CASPT2 and large atomic basis sets. It is found that CASPT2 and CC3 results are generally in very good agreement with one another (typical differences of ca. 3 × 10–3 A) when all electrons are correlated and when the aug-cc-pVTZ atomic basis set is employed with both methods. In a second stage, a statistical analysis reveals that, on the one hand, the excited-state (ES) bond lengths are much more sensitive to the selected level of theory than their ground-state (GS) counterparts and, on the other hand, that CCSDR(3) is probably the most cost-effective method delivering accurate structures. Indeed, CCSD tends to prov...

Properties of the water to boron nitride interaction: From zero to two dimensions with benchmark accuracy

Abstract: Molecular adsorption on surfaces plays an important part in catalysis, corrosion, desalination, and various other processes that are relevant to industry and in nature As a complement to experiments, accurate adsorption energies can be obtained using various sophisticated electronic structure methods that can now be applied to periodic systems The adsorption energy of water on boron nitride substrates, going from zero to 2-dimensional periodicity, is particularly interesting as it calls for an accurate treatment of polarizable electrostatics and dispersion interactions, as well as posing a practical challenge to experiments and electronic structure methods Here, we present reference adsorption energies, static polarizabilities, and dynamic polarizabilities, for water on BN substrates of varying size and dimension Adsorption energies are computed with coupled cluster theory, fixed-node quantum Monte Carlo (FNQMC), the random phase approximation, and second order Moller-Plesset theory These wavefunction based correlated methods are found to agree in molecular as well as periodic systems The best estimate of the water/h-BN adsorption energy is -107±7 meV from FNQMC In addition, the water adsorption energy on the BN substrates could be expected to grow monotonically with the size of the substrate due to increased dispersion interactions, but interestingly, this is not the case here This peculiar finding is explained using the static polarizabilities and molecular dispersion coefficients of the systems, as computed from time-dependent density functional theory (DFT) Dynamic as well as static polarizabilities are found to be highly anisotropic in these systems In addition, the many-body dispersion method in DFT emerges as a particularly useful estimation of finite size effects for other expensive, many-body wavefunction based methods

Accuracy of Coupled Cluster Excitation Energies in Diffuse Basis Sets

Abstract: We present a comprehensive statistical analysis on the accuracy of various excited state Coupled Cluster methods, accentuating the effect of diffuse basis sets on vertical excitation energies of valence and Rydberg-type states. Many popular approximate doubles and triples methods are benchmarked with basis sets up to aug-cc-pVTZ, with high level EOM-CCSDT results used as reference. The results reveal a serious deficiency of CC2 linear response and CIS(D) techniques in the description of Rydberg states, a feature not shown by the EOM-CCSD(2) and EOM-CCSD variants. The CC3 theory proves to be an accurate choice among the iterative approximate triples methods, while the novel perturbation-based CCSD(T)(a)* variant turns out to be the best way to include the effect of triple excitations in a noniterative way.