Coupled Cluster Methodology Research Articles

Analysis of chemical bonding of the ground and low-lying states of Mo2 and of Mo2Clx complexes, x = 2-10.

In this study, we perform accurate calculations via multireference configuration interaction and coupled cluster methodologies on the dimolybdenum molecule in conjunction with complete series of correlation and weighted core correlation consistent basis sets up to quintuple size. The bonding, the dissociation energies, and the spectroscopic parameters of the seven states that correlate with the ground state products are calculated. The ground state has a sextuple chemical bond, and each of the calculated excited states has one less bond than the previous state. The calculated values for the ground X1Σg + state of Mo2 have been extrapolated to the complete basis set limits. Our final values, re = 1.9324 Å and De (D0) = 4.502 ± 0.007(4.471 ± 0.009) eV, are in excellent agreement with the experimental values of re = 1.929, 1.938(9) Å and D0 = 4.476(10) eV. Mo2 in the Σg+13 state is a weakly bound dimer, forming 5s⋯5pz bonds, with De = 0.120eV at re = 3.53 Å. All calculated excited states (except Σg+13) have a highly multireference character (C0 = 0.25-0.55). The ordering of the molecular bonding orbitals changes as the spin is increased from quintet to septet state resulting in a change in energy separation ΔS,S-1 of the calculated states. The quite low bond dissociation energy of the ground state is due to the splitting of the molecular bonding orbitals in two groups differing in energy by ∼3eV. Finally, the bond breaking of Mo2, as the multiplicity of spin is increased, is analyzed in parallel with the Mo-Mo bond breaking in a series of Mo2Clx complexes when x is increased. Physical insight into the nature of the sextuple bond and its low dissociation energy is provided.

Molybdenum-Sulfur Bond: Electronic Structure of Low-Lying States of MoS.

The molybdenum-sulfur bond plays an important role in many processes such as nitrogen-fixation, and it is found as a building block in layered materials such as MoS2, known for its various shapes and morphologies. Here, we present an accurate theoretical and experimental investigation of the chemical bonding and the electronic structure of 20 low-lying states of the MoS molecule. Multireference and coupled cluster methodologies, namely, MRCISD, MRCISD + Q, RCCSD(T), and RCCSD[T], were employed in conjunction with basis sets up to aug-cc-pwCV5Z-PP/aug-cc-pwCV5Z for the study of these states. We note the significance of including the inner 4s24p6 electrons of Mo and 2s22p6 of S in the correlated space to obtain accurate results. Experimentally, the predissociation threshold of MoS was measured using resonant two-photon ionization spectroscopy, allowing for a precise measurement of the bond dissociation energy. Our extrapolated computational D0 value for the ground state is 3.936 eV, in excellent agreement with our experimental measurement of 3.932 ± 0.004 eV. The largest calculated adiabatic D0 (5.74 eV) and the largest dipole moment (6.50 D) were found for the 5Σ+ state, where a triple bond is formed. Finally, the connection of the chemical bonding of the isolated MoS species to the relevant solid, MoS2, is emphasized. The low-lying septet states of the diatomic molecule are involved in the material as a building block, explaining the stability and the variety of the shapes and morphologies of the material.

Guided Ion Beam Studies of the Thorium Monocarbonyl Cation Bond Dissociation Energy and Theoretical Unveiling of Different Isomers of [Th,O,C]+ and Their Rearrangement Mechanism.

Threshold collision-induced dissociation (TCID) of the thorium monocarbonyl cation, ThCO+, with xenon is performed using a guided ion beam tandem mass spectrometer. The only product observed is Th+ resulting from loss of the CO ligand. Analysis of the kinetic energy-dependent cross sections for this CID reaction yields the first experimental determination of the bond dissociation energy (BDE) of Th+-CO at 0 K as 0.94 ± 0.06 eV. Calculated BDEs at the CCSD(T) level of theory with cc-pVXZ (X = T and Q) basis sets and a complete basis set (CBS) extrapolation are in good agreement with the experimental result. The Feller-Peterson-Dixon composite coupled-cluster methodology was also applied on both ThCO+ and ThCO, with contributions up to CCSDT(Q) and a four-component treatment of spin-orbit coupling effects. The final 0 K Th+-CO BDE of 0.94 ± 0.04 eV is in excellent agreement with the current experimental result. The ionization energy of ThCO, as well as the atomization energies and heats of formation for both ThCO and ThCO+, is reported at this same level of theory. Complete potential energy profiles of both quartet and doublet spin are also constructed to elucidate the mechanism for the formation and interconversion of different isomers of [Th,O,C]+. Chemical bonding patterns in low-lying states of ThCO+ and potential energy curves for ThCO+ dissociation are also investigated.

Quadruple chemical bonding in the diatomic anions TcN- , RuC- , RhB- , and PdBe.

Quadruple bonding is uncommon for main group elements and the identification of species forming such bonds is remarkably interesting particularly in diatomic anions for which there is a lack of information. Here, it is found that the MX- anions, TcN- , RuC- , RhB- , and PdBe- , present quadruple bonding, as do the corresponding MX neutrals, even though a different type of σ2 bond is involved in ∑+ states of neutral and anions. Specifically, the ground states (X2 Δ or X2 ∑+ ) of the four anions and their first excited states (A2 ∑+ or A2 Δ) of TcN- , RuC- , and RhB- present quadruple bonds consisting of two σ and two π bonds: (4dz2 - 2pz )2 , 5pz 0 ← 2s2 , (4dxz - 2px )2 , and (4dyz - 2py )2 . Bond lengths, dissociation energies, spectroscopic data and electron affinities were calculated via high-level multireference and coupled-cluster methodology using the aug-cc-pV5ZX (-PP)M basis set. Strong bonding results in short bond lengths ranging from 1.602 (TcN- ) to 1.944 (PdBe- ) Å. Adiabatic (diabatic) binding energies reach up to 139 (184) kcal/mol. Electron affinities (EA) were calculated at 1.368 (TcN), 1.242 (RuC), 0.873 (RhB), 0.743 (PdBe) eV. Only for RhB has EA been measured experimentally at 0.961 eV, in good agreement with the value reported here.

Quadruple Bonding in the Ground and Low-Lying Excited States of the Diatomic Molecules TcN, RuC, RhB, and PdBe.

Multiple bonds between atoms are one of the most fundamental aspects of chemistry. Double and triple bonds are quite common, while quadruple bonds are a true oddity and very rare for the main group elements. Identifying molecules containing quadruple bonds is very important and, even more so, determining the necessary requirements for the existence of such bonds. Here we present high-level theoretical calculations on the isoelectronic MX molecules, i.e., TcN, RuC, RhB, and PdBe, showing that such a quadruple bond with main group elements is not that uncommon. We found that quadruple bonds are formed in their ground states X3Δ (TcN) and Χ1Σ+ (RuC, RhB, and PdBe) and in the two lowest excited states of TcN (1Σ+, 1Δ), RuC (1,3Δ), and RhB (1,3Δ). The quadruple bonds consist of two π and two σ bonds: (4dxz-2px)2, (4dyz-2py)2, (4dz2-2pz)2, and 5s0 ← 2s2 (1Σ+) or 5pz0←2s2 (1,3Δ). Bond lengths, dissociation energies, dipole moments, spectroscopic parameters, and relative energy ordering of the states were calculated via multireference and coupled cluster methodology using the aug-cc-pV5ZX(-PP)M basis sets. We study how the atomic states involved and how the gradual transition from covalent to dative bond, from TcN to PdBe, influence all of the calculated data, such as bond dissociation energies, bond lengths, and relative energy ordering of the states. Finally, we report the requirements for the occurrence of such bonds in molecular systems. All Be, B, C, and N atoms combining with the appropriate second-row transition metal can form quadruple bonds, while they cannot form such bonds with the first-row transition metals.

Rich Collection of n-Propylamine and Isopropylamine Conformers: Rotational Fingerprints and State-of-the-Art Quantum Chemical Investigation.

The conformational isomerism of isopropylamine and n-propylamine has been investigated by means of an integrated strategy combining high-level quantum-chemical calculations and high-resolution rotational spectroscopy. The equilibrium structures (and thus equilibrium rotational constants) as well as relative energies of all conformers have been computed using the so-called “cheap” composite scheme, which combines the coupled-cluster methodology with second-order Møller–Plesset perturbation theory for extrapolation to the complete basis set. Methods rooted in the density functional theory have been instead employed for computing spectroscopic parameters and for accounting for vibrational effects. Guided by quantum-chemical predictions, the rotational spectra of isopropylamine and n-propylamine have been investigated between 2 and 400 GHz with Fourier transform microwave and frequency-modulation millimeter/submillimeter spectrometers. Spectral assignments confirmed the presence of several conformers with comparable stability and pointed out possible Coriolis resonance effects between some of them.

Accurate nuclear quadrupole moment of ruthenium from the molecular method.

The nuclear electric quadrupole moment (NQM) of ruthenium was reevaluated by means of the molecular method. Therefore, four-component relativistic electronic structure calculations of the electric field gradient at the Ru nucleus in ruthenium monocarbide, which were done with the coupled cluster methodology and carefully augmented large basis sets, were combined with the respective nuclear quadrupole coupling constant from experiments. This provided a recommended NQM value of (425 ± 13) mbarn for 101Ru.

Accurate excited-state energetics by a combination of Monte Carlo sampling and equation-of-motion coupled-cluster computations.

The recently proposed idea of identifying the most important higher-than-doubly excited determinants in the ground-state coupled-cluster (CC) calculations through stochastic configuration interaction Quantum Monte Carlo propagations [J. E. Deustua et al., Phys. Rev. Lett. 119, 223003 (2017)] is extended to excited electronic states via the equation-of-motion (EOM) CC methodology. The advantages of the new approach are illustrated by calculations aimed at recovering the ground- and excited-state energies of the CH+ molecule at the equilibrium and stretched geometries resulting from the EOMCC calculations with a full treatment of singles, doubles, and triples.

Equation of motion approach for describing allowed transitions in Ne and Al3+ under classical and quantum plasmas

The equation of motion coupled cluster methodology within relativistic framework has been applied to analyze the electron correlation effects on the low lying dipole allowed excited states of Ne and Al3+ under classical and quantum plasma environments. The effect of confinement due to classical plasma has been incorporated through screened Coulomb potential, while that of quantum plasma has been treated by exponential cosine screened Coulomb potential. The confined structural properties investigated are the depression of ionization potential, low lying excitation energies (dipole allowed), oscillator strengths, transition probabilities, and frequency dependent polarizabilities under systematic variation of the plasma-atom coupling strength determined through the screening parameter. Specific atomic systems are chosen for their astrophysical importance and availability of experimental data related to laboratory plasma with special reference to Al3+ ion. Here, we consider 1s22s22p6(1S0)→1s22s22p5 ns/nd (1P1) (n=3,4) dipole allowed transitions of Ne and Al3+. Results for the free (isolated) atomic systems agree well with those available in the literature. Spectroscopic properties under confinement show systematic and interesting pattern with respect to plasma screening parameter.

Improving the accuracy of Møller-Plesset perturbation theory with neural networks.

Noncovalent interactions are of fundamental importance across the disciplines of chemistry, materials science, and biology. Quantum chemical calculations on noncovalently bound complexes, which allow for the quantification of properties such as binding energies and geometries, play an essential role in advancing our understanding of, and building models for, a vast array of complex processes involving molecular association or self-assembly. Because of its relatively modest computational cost, second-order Møller-Plesset perturbation (MP2) theory is one of the most widely used methods in quantum chemistry for studying noncovalent interactions. MP2 is, however, plagued by serious errors due to its incomplete treatment of electron correlation, especially when modeling van der Waals interactions and π-stacked complexes. Here we present spin-network-scaled MP2 (SNS-MP2), a new semi-empirical MP2-based method for dimer interaction-energy calculations. To correct for errors in MP2, SNS-MP2 uses quantum chemical features of the complex under study in conjunction with a neural network to reweight terms appearing in the total MP2 interaction energy. The method has been trained on a new data set consisting of over 200 000 complete basis set (CBS)-extrapolated coupled-cluster interaction energies, which are considered the gold standard for chemical accuracy. SNS-MP2 predicts gold-standard binding energies of unseen test compounds with a mean absolute error of 0.04 kcal mol-1 (root-mean-square error 0.09 kcal mol-1), a 6- to 7-fold improvement over MP2. To the best of our knowledge, its accuracy exceeds that of all extant density functional theory- and wavefunction-based methods of similar computational cost, and is very close to the intrinsic accuracy of our benchmark coupled-cluster methodology itself. Furthermore, SNS-MP2 provides reliable per-conformation confidence intervals on the predicted interaction energies, a feature not available from any alternative method.

Role of Spin States in Nitric Oxide Binding to Cobalt(II) and Manganese(II) Porphyrins. Is Tighter Binding Always Stronger?

Binding of nitric oxide (NO) to metalloporphyrins and heme groups is important in biochemistry while challenging to describe accurately by density functional theory (DFT) calculations. Here, the structural and thermochemical aspect of NO binding to Co(II) and Mn(II) porphyrins is investigated by DFT and DFT-D (dispersion-corrected) calculations, supported by reliable coupled-cluster methodology (CCSD(T)), and critically correlated with the experimental data. It is argued that whereas the bonding of NO to Co(II) porphyrin is a simple radical recombination, the bonding of NO to Mn(II) porphyrin is accompanied by a crossing of spin states. For this reason, the spin-state conversion energy contributes to the Mn-NO bond energy, and the paradigmatic correlation between bond length and bond energy is violated for the considered nitrosyl complexes: the Mn-NO bond is (structurally) shorter by ∼0.2 Å, albeit (energetically) weaker by a few kcal/mol, compared with the Co-NO bond. Moreover, none of the many tested DFT methods can reproduce the Co-NO and Mn-NO bond energies simultaneously, except for calculations with B3LYP*-D3, TPSSh-D3, and M06-D3 methods supplemented with the proposed spin-state energy correction (to compensate for an error on the calculated spin-state conversion energy). The results of this study are important to appreciate the role of spin-state changes in ligand binding properties of heme-related models. They also highlight the need for accurate calculations for correct interpretation of experimental data, including the qualitative structure-energy relationship.

The role of core–valence electron correlation in gallium halides: a comparison of composite methods

The electronic structure and atomization energies of gas phase gallium halides (GaXn where X = F, Cl, Br, and I, and n = 1 … 3) are studied with highly accurate ab initio composite methods. Coupled cluster methodologies up to full hextuples (CCSDTQPH) are used to compute spectroscopic properties of GaF, which are compared with experiment and conventional levels of theory [such as complete basis set CCSD(T)]. An appropriate treatment of core–valence electron correlation is necessary to obtain reasonable geometries and atomization energies. More efficient composite methods such as the correlation consistent Composite Approach (ccCA, ccCA-TM, rp-ccCA) and the Gaussian-n methods [G3, G3(MP2), G4, G4(MP2)] are calibrated to explore application toward large GaXn-containing molecules relevant to catalysis. For the 12 GaXn compounds, ccCA-TM and rp-ccCA with Boys-localized molecular orbitals has a mean absolute deviation of 1.41 kcal mol−1 compared to complete basis set CCSD(T). However, the G3(MP2) method performs better for complexes with the lighter halides. Calibration of GaXn (X = F, Cl, Br, and I; n = 1–3) ab initio atomization energies is useful to improve prediction of ligand binding energies in novel gallium halide-containing catalysts. Inorganic and organometallic complexes with GaXn ligands are extremely difficult to synthesize and characterize. Therefore, rational design based on well-understood theory is essential.

Global ab initio potential energy surface for the O2((3)Σ(g)(-)) + N2((1)Σ(g)(-)) interaction. Applications to the collisional, spectroscopic, and thermodynamic properties of the complex.

A detailed characterization of the interaction between the most abundant molecules in air is important for the understanding of a variety of phenomena in atmospherical science. A completely ab initio global potential energy surface (PES) for the O2((3)Σg(–)) + N2((1)Σg(+)) interaction is reported for the first time. It has been obtained with the symmetry-adapted perturbation theory utilizing a density functional description of monomers [SAPT(DFT)] extended to treat the interaction involving high-spin open-shell complexes. The computed interaction energies of the complex are in a good agreement with those obtained by using the spin-restricted coupled cluster methodology with singles, doubles, and noniterative triple excitations [RCCSD(T)]. A spherical harmonics expansion of the interaction potential containing a large number of terms due to the anisotropy of the interaction has been built from the ab initio data. The expansion coefficients, which are functions of the intermolecular distance, are matched in the long-range with the analytical functions based on the recent ab initio calculations of the electric properties of the monomers [M. Bartolomei et al. J. Comput. Chem. 2011, 32, 279]. The PES is tested against the second virial coefficient B(T) data and the integral cross sections measured with rotationally hot effusive beams, leading in both cases to a very good agreement. The lowest lying states of the complex have been computed and relevant spectroscopic features of the interacting complex are reported. A comparison with a previous experimentally derived PES is also provided.

Rovibrational energies of B2H2([formula omitted]) from an explicitly correlated potential energy surface

The six-dimensional potential energy surface of the X∼3Σg- electronic ground state of B2H2 was determined using spin-unrestricted explicitly correlated coupled cluster methodology. The analytic representation of this surface was used to compute the rovibrational energies of this boron hydride dimer. For the 11B2H2 species, the antisymmetric B–H stretching frequency is computed at 2693.2cm−1, and an isotopic shift of +10.7cm−1 is deduced for 10B2H2. Comparisons with the electronic ground state of diatomic fragments B2 and BH are discussed. The J=1←0 rotational transition is calculated at 50511.5MHz for 11B2H2 and at 53551.0MHz for 10B2H2. Spectroscopic constants of the deuterated isotopologues are reported.

Ground and excited states of vanadium hydroxide isomers and their cations, VOH0,+ and HVO0,+

Employing correlation consistent basis sets of quadruple-zeta quality and applying both multireference configuration interaction and single-reference coupled cluster methodologies, we studied the electronic and geometrical structure of the [V,O,H](0,+) species. The electronic structure of HVO(0,+) is explained by considering a hydrogen atom approaching VO(0,+), while VOH(0,+) molecules are viewed in terms of the interaction of V(+,2+) with OH(-). The potential energy curves for H-VO(0,+) and V(0,+)-OH have been constructed as functions of the distance between the interacting subunits, and the potential energy curves have also been determined as functions of the H-V-O angle. For the stationary points that we have located, we report energies, geometries, harmonic frequencies, and dipole moments. We find that the most stable bent HVO(0,+) structure is lower in energy than any of the linear HVO(0,+) structures. Similarly, the most stable state of bent VOH is lower in energy than the linear structures, but linear VOH(+) is lower in energy than bent VOH(+). The global minimum on the potential energy surface for the neutral species is the X(3)A" state of bent HVO, although the X(5)A" state of bent VOH is less than 5 kcal/mol higher in energy. The global minimum on the potential surface for the cation is the X(4)Σ(-) state of linear VOH(+), with bent VOH(+) and bent HVO(+) both more than 10 kcal/mol higher in energy. For the neutral species, the bent geometries exhibit significantly higher dipole moments than the linear structures.

Electronic states and rovibrational spectroscopy of the HAlF+ and HAlCl+ cations

Ab initio calculations have been performed to investigate the nature of the low-lying electronic states and the rovibrational energy levels of the electronic ground state of HAlF+ and HAlCl+. The one-dimensional cuts of the low-lying states of both cations have been investigated at the complete active space self-consistent field level, revealing the single-configuration nature of the electronic ground states. Using explicitly correlated coupled-cluster methodology and core-valence basis sets, the three-dimensional potential energy surfaces of both species have then been generated, and the rovibrational energy levels were computed variationally. The analysis of the results reveals the similar nature of the Al–H bond in both species, according to their equilibrium bond lengths and to the Al–H stretching mode frequencies. The rovibrational energy levels of the deuterated isotopologues are also presented.

New ab initio study of the spectroscopy of HCNH +

Highly correlated ab initio computations have been performed to investigate the rovibrational energy levels and the rotational transitions of the HCNH + cation and its isotopologues. Using explicitly correlated coupled-cluster methodology and core-valence basis sets, the six-dimensional potential energy surface of the electronic ground state of this ion has been generated. The resulting analytical representation has been used in the full-dimensional variational calculations of the rovibrational energy levels. For all of the isotopologues, the fundamental modes are found to be in close agreement with the available experimental data, and reliable predictions are given for those modes that are not observed experimentally. The rotational transitions, up to the J = 10 value of the total angular momentum quantum number, have also been calculated. The rotational transitions obtained computationally are compared with the values deduced from laboratory experiments or interstellar media detections. Some of these results are predictive, especially those for DCNH + and H 13CNH +. Finally, we provide a theoretical simulation of the rotational spectra for these species at 5 K, 7 K, and 10 K.

Combustion Chemistry: Important Features of the C3H5 Potential Energy Surface, Including Allyl Radical, Propargyl + H2, Allene + H, and Eight Transition States

The C(3)H(5) potential energy surface (PES) encompasses molecules of great significance to hydrocarbon combustion, including the resonantly stabilized free radicals propargyl (plus H(2)) and allyl. In this work, we investigate the interconversions that take place on this PES using high level coupled cluster methodology. Accurate geometries are obtained using coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)] combined with Dunning's correlation consistent quadruple-ζ basis set cc-pVQZ. The energies for these stationary points are then refined by a systematic series of computations, within the focal point scheme, using the cc-pVXZ (X = D, T, Q, 5, 6) basis sets and correlation treatments as extensive as coupled cluster with full single, double, and triple excitation and perturbative quadruple excitations [CCSDT(Q)]. Our benchmarks provide a zero-point vibrational energy (ZPVE) corrected barrier of 10.0 kcal mol(-1) for conversion of allene + H to propargyl + H(2). We also find that the barrier for H addition to a terminal carbon atom in allene leading to propenyl is 1.8 kcal mol(-1) lower than that for the addition to a central atom to form the allyl radical.

Theoretical spectroscopy of the HNCl− anion

Ab initio computations have been performed to investigate the stability and the spectroscopy of the HNCl− anion. Using explicitly correlated coupled-cluster methodology and core-valence basis set, the linear–bent path of the neutral and anionic molecules have been computed, and the adiabatic electron affinity of HNCl has been deduced at 1.29 eV. The three-dimensional potential energy surface of the neutral HNCl () and of the HNCl− () anion have also been generated using the same computational approach, and their analytical representations have been used for the variational determination of their rovibrational energy levels. Our computations reveal the localization of the additional electron into an anti-bounding molecular orbital associated with the N–Cl bond. The modelling of the photoelectron spectrum of HNCl− and DNCl− is also presented, showing the vibrational progression associated with the N–Cl stretching mode.

An efficient route to thermal rate constants in reduced dimensional quantum scattering simulations: Applications to the abstraction of hydrogen from alkanes

We present an efficient approach to the determination of two-dimensional potential energy surfaces for use in quantum reactive scattering simulations. Our method involves first determining the minimum energy path (MEP) for the reaction by means of an ab initio intrinsic reaction coordinate calculation. This one-dimensional potential is then corrected to take into account the zero point energies of the spectator modes. These are determined from Hessians in curvilinear coordinates after projecting out the modes to be explicitly treated in quantum scattering calculations. The final (1+1)-dimensional potential is constructed by harmonic expansion about each point along the MEP before transforming the whole surface to hyperspherical coordinates for use in the two-dimensional scattering simulations. This new method is applied to H-atom abstraction from methane, ethane and propane. For the latter, both reactive channels (producing i-C(3)H(7) or n-C(3)H(7)) are investigated. For all reactions, electronic structure calculations are performed using an efficient, explicitly correlated, coupled cluster methodology (CCSD(T)-F12). Calculated thermal rate constants are compared to experimental and previous theoretical results.