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At least 343 records · Page 19

A promising intersection of excited‐state‐specific methods from quantum chemistry and quantum Monte Carlo

Abstract We present a discussion of recent progress in excited‐state‐specific quantum chemistry and quantum Monte Carlo alongside a demonstration of how a combination of methods from these two fields can offer reliably accurate excited state predictions across singly excited, doubly excited, and charge transfer states. Both of these fields have seen important advances supporting excited state simulation in recent years, including the introduction of more effective excited‐state‐specific optimization methods, improved handling of complicated wave function forms, and ways of explicitly balancing the quality of wave functions for ground and excited states. To emphasize the promise that exists at this intersection, we provide demonstrations using a combination of excited‐state‐specific complete active space self‐consistent field theory, selected configuration interaction, and state‐specific variance minimization. These demonstrations show that combining excited‐state‐specific quantum chemistry and variational Monte Carlo can be more reliably accurate than either equation of motion coupled cluster theory or multi‐reference perturbation theory, and that it can offer new clarity in cases where existing high‐level methods do not agree. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry

Otis, Leon↗

Theoretical kinetics predictions for NH 2 + HO 2

Recent modeling studies of NH 3 oxidation, which are motivated by the prospective role of ammonia as a zero-carbon fuel, have indicated significant discrepancies between existing literature mechanisms. In this study high level theoretical kinetics predictions have been obtained for the reaction of NH 2 with HO 2 , which has previously been highlighted as an important reaction with high sensitivity and high uncertainty. The potential energy surface is explored with coupled cluster calculations including large basis sets and high-level corrections to yield high accuracy (~0.2 kcal/mol) estimates of the stationary point energies. Variational transition state theory is used to predict the microcanonical rate constants, which are then incorporated in master equation treatments of the temperature and pressure dependent kinetics. For the radical-radical channels, the microcanonical rates are obtained from variable reaction coordinate transition state theory implementing directly evaluated multireference electronic energies. The analysis yields predictions for the total rate constant as well as the branching to the NH 3 + O 2 , H 2 NO + OH, and HNO + H 2 O channels. Rate constants are also reported for the H 2 NO + OH reaction as they arise naturally from the analysis. The rate constant and branching fraction determined in this work for the NH 2 + HO 2 reaction deviate significantly from values used in most previous modeling studies. The fact that the main product channel is chain terminating, rather than propagating, has strong implications for modeling NH 3 ignition and oxidation, in particular at intermediate temperatures and elevated pressure.

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From electronic structure to model application of key reactions for gasoline/alcohol combustion: Hydrogen-atom abstractions by $CH_3\dot{O}$ radical

H-atom abstraction by methoxy radical ($CH_3\dot{O}$) plays an important role in capturing the kinetics of reactions between gasoline components and alcohols. This study focuses on determining the reaction rates and thermodynamic properties of methoxy radical reactions with five gasoline fuel components: n-heptane, iso-octane, 1-hexene, cyclopentane and toluene. Electronic structure calculations were per-formed for all the stationary points with M06-2X/6 -311 ++ g(d,p) method. G3 composite method with atomization method is used for determining Δ f H 0 of all the closed shell and radical species, using which the necessary thermodynamic data of all the species was determined. Coupled cluster theory QCISD(T)/cc-pVXZ (where X = D and T) and Møller-Plesset perturbation theory MP2/cc-pVXZ (where X = D, T and Q) were used to calculate single point energies. Subsequently, rate constants for all hydrogen atom ab-straction channels have been performed using conventional transition state theory with unsymmetric tunneling corrections. A systematic comparison of rates for abstraction from different sites within the same species and same site from different species is done in order to get insights into this reaction class. Here, the computed thermodynamic properties and rate constants were incorporated into a recent gasoline mechanism to investigate the impact of the calculations performed in this work. A shift in predicted NTC (negative temperature coefficient) behavior and significant reduction in model reactivity is observed upon incorporating the rates calculated herein.

33 ADVANCED PROPULSION SYSTEMS↗

Photoionization energetics and dissociation pathways of hydroperoxyethyl formate produced in the reaction of CH 3 CHOO + formic acid

The bimolecular reaction of Criegee intermediates, zwitterionic carbonyl oxide species produced in alkene ozonolysis, with organic acids leads to formation of functional hydroperoxides implicated in the generation of atmospheric aerosols. This theoretical study using high-level explicitly correlated coupled-cluster theory examines the low energy conformers of hydroperoxyethyl formate [HOOCH(CH 3 )OCHO, HPEF] formed in the bimolecular reaction of CH 3 CHOO, a simple alkyl-substituted Criegee intermediate, with formic acid, and the detection of HPEF via photoionization. Here, the vertical and adiabatic ionization energies of HPEF are computed, along with the pathways for dissociative ionization that produce HO 2 or OCHO fragments with daughter ions.

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Sequential Bond Dissociation Energies of Th + (CO) x , x = 3–6: Guided Ion Beam Collision-Induced Dissociation and Quantum Computational Studies

Collision-induced dissociation (CID) of [Th,xC,xO] + , x = 3–6, with Xe is performed using a guided ion beam tandem mass spectrometer (GIBMS). Products are formed exclusively by the loss of CO ligands. Analyses of the kinetic energy-dependent CID product cross sections yield bond dissociation energies (BDEs) of (CO) x–1 Th + –CO at 0 K as 1.09 ± 0.05, 0.82 ± 0.07, 0.63 ± 0.05, and 0.70 ± 0.05 eV, respectively. Different structures of [Th,xC,xO] + were explored using various electronic structure methods, and BDEs for CO ligand loss from precursor [Th,xC,xO] + complexes were computed. Both experimental and theoretical results corroborate that the structures of [Th,xC,xO] + , x = 3–6, formed experimentally are homoleptic thorium cation carbonyl complexes, Th + (CO) x . The nonmonotonic trend in experimental BDEs is reproduced theoretically, although ambiguities in the spin states of the x = 4–6 complexes (doublet or quartet) remain. BDEs calculated at the coupled cluster with single, double, and perturbative triple excitations (CCSD(T))/cc-pVXZ//B3LYP/cc-PVXZ (X = T and Q) level and a complete basis set (CBS) extrapolation agree reasonably well with the experimental values for all complexes. Thorium oxide ketenylidene carbonyl cations, OTh + CCO(CO) y , y = 1–4, were calculated to be the most stable structures of [Th,xC,xO] + , x = 3–6, respectively; however, these are not observed in our experiment. Potential energy profiles (PEPs) having either quartet or doublet spin calculated at the B3LYP/cc-pVQZ level suggest that the failure to observe OTh + CCO(CO) y , y = 1–4, is the result of a barrier corresponding to the C–C bond formation, making the formation of OTh + CCO(CO) y inaccessible kinetically under the present experimental conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Alkali Metal Control of Triplet-Mediated C–H Activation in Iron-Mediated Coupling of Dinitrogen and Benzene

Direct coupling of N 2 with abundant feedstocks like benzene to form N-containing organic compounds is a promising strategy for N 2 fixation pathways. The challenge of coupling N 2 activation and C–H bond oxidative addition was recently solved by introducing a reversible benzene C–H bond activation process mediated by a low-valent Fe(0) complex, which gave an organometallic product that could couple with partially reduced N 2 . Interestingly, the energetics of the C–H oxidative addition/reductive elimination step depends on the choice of alkali metal. However, the reason why the alkali metal influences the C–H bond activation remained elusive. In this work, we present a comprehensive study on this Fe(0)-mediated reversible C–H activation. Through density functional theory combined with high-level coupled cluster calculations, we discovered that the intermediate-spin triplet (S = 1) controls the energy of the transition state for C–H cleavage, while the high-spin quintet (S = 2) controls the position of the equilibrium. Na + drives the equilibrium toward oxidative addition due to an electrostatic effect, while K + and Rb + are dominated by a steric effect that favors the iron(0) species. The key role played by nonbonding interactions in the Fe-mediated C–H activation provides a conceptual model for alkali control over organometallic transformations.

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A Computational Assessment of Actinide Dioxide Cations AnO 2 2+ for An = U to Lr: The Limited Stability Range of the Hexavalent Actinyl Moiety, [O=An=O] 2+

The isolated gas-phase actinide dioxide dications, AnO 2 2+ , were evaluated by DFT and coupled cluster CCSD(T) calculations for 12 actinides, An = U–Lr. CASSCF calculations were used to define the orbitals for the CCSD(T) calculations. The characteristic linear [O$=$An$=$O] 2+ hexavalent actinyl(VI) was found to be the lowest energy structure for An = U, Np, and Pu, which also form stable actinyl(VI) species in solution and possibly for Am when spin–orbit effects are included. For Am, there is a divalent [An II (O 2 )] 2+ structure where the dioxygen is an end-on physisorbed η 1 - 3 O 2 2 kcal/mol above the actinyl when spin–orbit effects are included which lower the energy of the actinyl structure. For An = Cm, Bk, and Lr, the lowest energy structure is trivalent [An III (O 2 – )] 2+ where the dioxygen is a side-on superoxide, η 2 -O 2 – . For Cm, the actinyl is close in energy to the ground state when spin–orbit effects are included. For An = Cf, Es, Fm, Md, and No, the lowest energy structure is divalent [An II (O 2 )] 2+ where the dioxygen is an end-on physisorbed η 1 - 3 O 2 . The relative energies suggest that curyl(VI) and berkelyl(VI), like well-known americyl(VI), might be stabilized by coordinating ligands in condensed phases. The results further indicate that for californyl and beyond, the actinyl(VI) moieties will probably be elusive even using strong donor ligands. The prevalence of low oxidation states (OSs) An(II) and An(III) for transplutonium actinides reflects stabilization of the 5f orbitals and validates established trends, including the remarkably high stability of divalent No. Finally, bond distances and other parameters suggest maximum bond covalency around plutonyl(VI), with a particularly substantial decrease in bond strength between americyl(VI) and curyl(VI).

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Improving Bond Dissociations of Reactive Machine Learning Potentials through Physics-Constrained Data Augmentation

In the field of computational chemistry, predicting bond dissociation energies (BDEs) presents well-known challenges, particularly due to the multireference character of reactive systems. Many chemical reactions involve configurations where single-reference methods fall short, as the electronic structure can significantly change during bond breaking. As generating training data for partially broken bonds is a challenging task, even state-of-the-art reactive machine learning interatomic potentials (MLIPs) often fail to predict reliable BDEs and smooth dissociation curves. By contrast, simple and inexpensive physics-based models, such as the well-established Morse potential, do not suffer from any such limitations. This work leverages the Morse potential to improve reactive MLIPs by augmenting the training data set with inexpensive Morse data along the dissociation pathways. Further, this physics-constrained data augmentation (PCDA) approach results in MLIPs with smooth bond dissociation curves as well as near coupled-cluster level BDEs, all without requiring any expensive multireference quantum mechanical calculations. A case study for methane combustion demonstrates how the PCDA approach can improve an existing reactive MLIP, namely, ANI-1xnr. In conclusion, not only are the BDEs and bond dissociation curves for all radicals and molecules significantly improved compared to ANI-1xnr but the PCDA-trained MLIP retains the reliability of ANI-1xnr when performing reactive molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Utilizing Essential Symmetry Breaking in Auxiliary-Field Quantum Monte Carlo: Application to the Spin Gaps of the C 36 Fullerene and an Iron Porphyrin Model Complex

We present three distinct examples where phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can be reliably performed with a single-determinant trial wave function with essential symmetry breaking. Essential symmetry breaking was first introduced by Lee and Head-Gordon [ Phys. Chem. Chem. Phys. 2019, 21, 4763-4778, 10.1039/C8CP07613H]. We utilized essential complex and time-reversal symmetry breaking with ph-AFQMC to compute the triplet–singlet energy gap in the TS12 set. We found statistically better performance of ph-AFQMC with complex-restricted orbitals than with spin-unrestricted orbitals. We then showed the utilization of essential spin symmetry breaking when computing the singlet–triplet gap of a known biradicaloid, C 36 . ph-AFQMC with spin-unrestricted Hartree–Fock (ph-AFQMC+UHF) fails catastrophically even with spin-projection and predicts no biradicaloid character. With approximate Brueckner orbitals obtained from regularized orbital-optimized second-order Møller–Plesset perturbation theory (κ-OOMP2), ph-AFQMC quantitatively captures strong biradicaloid character of C 36 . Lastly, we applied ph-AFQMC to the computation of the quintet–triplet gap in a model iron porphyrin complex where brute-force methods with a small active space fail to capture the triplet ground state. We show unambiguously that neither triplet nor quintet is strongly correlated using UHF, κ-OOMP2, and coupled-cluster with singles and doubles (CCSD) performed on UHF and κ-OOMP2 orbitals. There is no essential symmetry breaking in this problem. By virtue of this, we were able to perform UHF+ph-AFQMC reliably with a cc-pVTZ basis set and predicted a triplet ground state for this model geometry. The largest ph-AFQMC in this work correlated 186 electrons in 956 orbitals. Our work highlights the utility, scalability, and accuracy of ph-AFQMC with a single-determinant trial wave function with essential symmetry breaking for systems mainly dominated by dynamical correlation with little static correlation.

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Density Functionals for Hydrogen Storage: Defining the H2Bind275 Test Set with Ab Initio Benchmarks and Assessment of 55 Functionals

Efficient and high-capacity storage materials are indispensable for a hydrogen-based economy. In silico tools can accelerate the process of discovery of new adsorbent materials with optimal hydrogen adsorption enthalpies. Density functional theory is well-poised to become a very useful tool for enabling high-throughput screening of potential materials. In this work, we have identified density functional approximations that provide good performance for hydrogen binding applications following a two-pronged approach. First, we have compiled a data set (H2Bind275) that comprehensively represents the hydrogen binding problem capturing the chemical and mechanistic diversity in the binding sites encountered in hydrogen storage materials. We have also computed reference interaction energies for this data set using coupled-cluster theory. Second, we have assessed the performance of 55 density functional approximations for predicting H 2 interaction energies and have identified two hybrid density functionals (ωB97X-V and ωB97M-V), two double hybrid density functionals (DSD-PBEPBE-D3(BJ) and PBE0-DH), and one semilocal density functional (B97M-V) as the best performing ones. We have recommended the addition of empirical dispersion corrections to systematically underbinding density functionals such as revPBE, BLYP, and B3LYP for improvements in performance at negligible additional cost. We have also recommended the usage of the def2-TZVPP basis set as it represents a good compromise between accuracy and cost, limiting the finite basis set errors to less than 1 kJ/mol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

N 5 -Scaling Excited-State-Specific Perturbation Theory

In this paper, we show that by working in a basis similar to that of the natural transition orbitals and using a modified zeroth-order Hamiltonian, the cost of a recently introduced perturbative correction to excited-state mean field theory can be reduced from seventh to fifth order in the system size. The (occupied) 2 (virtual) 3 asymptotic scaling matches that of ground-state second-order Møller-Plesset theory but with a significantly higher prefactor because the bottleneck is iterative: it appears in the Krylov-subspace-based solution of the linear equation that yields the first-order wave function. Here, we discuss the details of the modified zeroth-order Hamiltonian we use to reduce the cost and the automatic code generation process we used to derive and verify the cost scaling of the different terms. Overall, we find that our modifications have little impact on the method's accuracy, which remains competitive with singles and doubles equation-of-motion coupled cluster.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficient Step-Merged Quantum Imaginary Time Evolution Algorithm for Quantum Chemistry

In this work, we develop a resource-efficient step-merged quantum imaginary time evolution approach (smQITE) to solve for the ground state of a Hamiltonian on quantum computers. This heuristic method features a fixed shallow quantum circuit depth along the state evolution path. We use this algorithm to determine the binding energy curves of a set of molecules, including H 2 , H 4 , H 6 , LiH, HF, H 2 O, and BeH 2 , and find highly accurate results. The required quantum resources of smQITE calculations can be further reduced by adopting the circuit form of the variational quantum eigensolver (VQE) technique, such as the unitary coupled cluster ansatz. We demonstrate that smQITE achieves a similar computational accuracy as VQE at the same fixed-circuit ansatz, without requiring a generally complicated high-dimensional nonconvex optimization. Finally, smQITE calculations are carried out on Rigetti quantum processing units, demonstrating that the approach is readily applicable on current noisy intermediate-scale quantum devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Third-Order Møller–Plesset Theory Made More Useful? The Role of Density Functional Theory Orbitals

The practical utility of Møller–Plesset (MP) perturbation theory is severely constrained by the use of Hartree–Fock (HF) orbitals. It has recently been shown that the use of regularized orbital-optimized MP2 orbitals and scaling of MP3 energy could lead to a significant reduction in MP3 error. In this work, we examine whether density functional theory (DFT)-optimized orbitals can be similarly employed to improve the performance of MP theory at both the MP2 and MP3 levels. We find that the use of DFT orbitals leads to significantly improved performance for prediction of thermochemistry, barrier heights, noncovalent interactions, and dipole moments relative to the standard HF-based MP theory. Indeed, MP3 (with or without scaling) with DFT orbitals is found to surpass the accuracy of coupled-cluster singles and doubles (CCSD) for several data sets. We also found that the results are not particularly functional sensitive in most cases (although range-separated hybrid functionals with low delocalization error perform the best). As such, MP3 based on DFT orbitals thus appears to be an efficient, noniterative O(N 6 ) scaling wave-function approach for single-reference electronic structure computations. Scaled MP2 with DFT orbitals is also found to be quite accurate in many cases, although modern double hybrid functionals are likely to be considerably more accurate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Massively Parallel Implementation of the CCSD(T) Method Using the Resolution-of-the-Identity Approximation and a Hybrid Distributed/Shared Memory Parallelization Model

In this work, a parallel algorithm is described for the coupled-cluster singles and doubles method augmented with a perturbative correction for triple excitations [CCSD(T)] using the resolution-of-the-identity (RI) approximation for two-electron repulsion integrals (ERIs). The algorithm bypasses the storage of four-center ERIs by adopting an integral-direct strategy. The CCSD amplitude equations are given in a compact quasi-linear form by factorizing them in terms of amplitude-dressed three-center intermediates. A hybrid MPI/OpenMP parallelization scheme is employed, which uses the OpenMP-based shared memory model for intranode parallelization and the MPI-based distributed memory model for internode parallelization. Parallel efficiency has been optimized for all terms in the CCSD amplitude equations. Two different algorithms have been implemented for the rate-limiting terms in the CCSD amplitude equations that entail and -scaling computational costs, where N O and N V denote the number of correlated occupied and virtual orbitals, respectively. One of the algorithms assembles the four-center ERIs requiring N V 4 and N O 2 N V 2 -scaling memory costs in a distributed manner on a number of MPI ranks, while the other algorithm completely bypasses the assembling of quartic memory-scaling ERIs and thus largely reduces the memory demand. It is demonstrated that the former memory-expensive algorithm is faster on a few hundred cores, while the latter memory-economic algorithm shows a better strong scaling in the limit of a few thousand cores. The program is shown to exhibit a near-linear scaling, in particular for the compute-intensive triples correction step, on up to 8000 cores. The performance of the program is demonstrated via calculations involving molecules with 24–51 atoms and up to 1624 atomic basis functions. As the first application, the complete basis set (CBS) limit for the interaction energy of the π-stacked uracil dimer from the S66 data set has been investigated. This work reports the first calculation of the interaction energy at the CCSD(T)/aug-cc-pVQZ level without local orbital approximation. The CBS limit for the CCSD correlation contribution to the interaction energy was found to be -8.01 kcal/mol, which agrees very well with the value -7.99 kcal/mol reported by Schmitz, Hättig, and Tew [ Phys. Chem. Chem. Phys. 2014 , 16 , 22167-22178]. The CBS limit for the total interaction energy was estimated to be -9.64 kcal/mol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron–electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. In conclusion, the transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Route to Chemical Accuracy for Computational Uranium Thermochemistry

Benchmark spinor-based relativistic coupled-cluster calculations for the ionization energies of the uranium atom, the uranium monoxide molecule (UO), and the uranium dioxide molecule (UO 2 ) and for the bond dissociation energies of UO and UO 2 are reported. The accuracy of these calculations in the treatments of relativistic, electron correlation, and basis-set effects is analyzed. Furthermore, the intrinsic convergence of the computed results and the favorable comparison with the experimental values demonstrate the unique applicability of the spinor representation of quantum-chemical methods to open-shell uranium-containing atomic and molecular species with uranium oxidation states ranging from U(0) to U(V).

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Quantum Simulations of Fermionic Hamiltonians with Efficient Encoding and Ansatz Schemes

Here, we propose a computational protocol for quantum simulations of fermionic Hamiltonians on a quantum computer, enabling calculations on spin defect systems which were previously not feasible using conventional encodings and a unitary coupled-cluster ansatz of variational quantum eigensolvers. We combine a qubit-efficient encoding scheme mapping Slater determinants onto qubits with a modified qubitcoupled cluster ansatz and noise-mitigation techniques. Our strategy leads to a substantial improvement in the scaling of circuit gate counts and in the number of required qubits, and to a decrease in the number of required variational parameters, thus increasing the resilience to noise. We present results for spin defects of interest for quantum technologies, going beyond minimum models for the negatively charged nitrogen vacancy center in diamonds and the double vacancy in 4H silicon carbide (4H-SiC) and tackling a defect as complex as negatively charged silicon vacancy in 4H-SiC for the first time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures

The primary focus of GAMESS over the last 5 years has been the development of new high-performance codes that are able to take effective and efficient advantage of the most advanced computer architectures, both CPU and accelerators. These efforts include employing density fitting and fragmentation methods to reduce the high scaling of well-correlated (e.g., coupled-cluster) methods as well as developing novel codes that can take optimal advantage of graphical processing units and other modern accelerators. Because accurate wave functions can be very complex, an important new functionality in GAMESS is the quasi-atomic orbital analysis, an unbiased approach to the understanding of covalent bonds embedded in the wave function. Finally, best practices for the maintenance and distribution of GAMESS are also discussed.

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