Multireference Averaged Coupled-pair Functional Research Articles

Semi-empirical dipole moment of carbon monoxide and line lists for all its isotopologues revisited

The semi-empirical permanent electric dipole-moment function (DMF) for the ground state of the CO molecule has been reconstructed analytically in the entire range of the inter-nuclear distance r∈[0,+∞) by means of the simultaneous non-linear least-squares fitting (NLLSF) of the selected experimental intensities for the main 12C16O isotopologue (including those with sub-percent uncertainties) and the ab initio permanent dipole moment. The ab initio DMFs were evaluated using single-reference coupled cluster (SR-CCSD(T)) and multi-reference averaged coupled-pair functional (MR-ACPF) methods. The ab initio data were involved in the NLLSF procedure to propagating smoothly the semi-empirical DMF outside the local region covered by the experimental intensities for the lowest vibrational v′≤11 levels. The derived mass-invariant DMF possesses the physically correct asymptotic behavior in both the united-atom and dissociation limits as well as reproduces the vast majority of the measured intensities in v″=0→v′∈[0,6] and v″=1→v′=4,5 bands within their experimental uncertainties. The resulting DMF and the mass-corrected potential-energy function of Meshkov et al. (2018)[16] were used to upgrade line lists for all CO isotopologues in the wide range of vibrational and rotational quantum numbers v∈[0,41],Δv∈[0,6], J∈[0,150] (J∈[0,200] for the 0-0 and 1-0 bands). The predicted intensities are compared with their experimental counterparts, which were not involved in the present NLLSF, to highlight presumable random and systematic errors in the measured data; in particular, the intensities in the “abnormal” 0→5 band of the 12C16O isotopologue and some other bands of minor isotopologues should be revisited experimentally. The resultant line list should be considered superior to previous efforts in terms of accuracy.

Ground-state potential energy functions and vibration-rotation energy levels of beryllium lithium and its cation.

The accurate ground-state potential energy functions of the beryllium lithium dimer, BeLi, and its cation, BeLi+ , have been determined from ab initio calculations using the multi-reference averaged coupled-pair functional (MR-ACPF) method in conjunction with the correlation-consistent core-valence basis sets up to septuple-zeta quality. The importance of the electron correlation beyond the MR-ACPF level of approximation, scalar relativistic, and adiabatic effects was discussed. For BeLi+ , the similar calculation was performed using the single-reference coupled-cluster method, up to the CCSDTQ level of approximation. The vibration-rotation energy levels of the two species were predicted to near the "spectroscopic" accuracy. Strangely enough, the predicted vibrational term values do not compare well with the recent experimental data for either BeLi or BeLi+ , with discrepancies reaching as much as 20-60 cm-1 for highly excited vibrational levels.

Ab Initio Ground-State Potential Energy Function and Vibration-Rotation Energy Levels of Aluminum Monohydride.

The accurate ground-state potential energy function of aluminum monohydride (AlH) has been determined from ab initio calculations using the multireference averaged coupled-pair functional (MR-ACPF) method in conjunction with the correlation-consistent core-valence basis sets up to septuple-zeta quality. The vibration-rotation energy levels of the two isotopologues, AlH and AlD, were predicted to near the "spectroscopic" accuracy. The importance of electron correlation beyond the MR-ACPF level of approximation, the scalar relativistic, spin-orbit, adiabatic, and nonadiabatic effects was discussed. © 2019 Wiley Periodicals, Inc.

Ab initio ground-state potential energy function and vibration-rotation energy levels of imidogen, NH.

The accurate ground-state potential energy function of imidogen, NH, has been determined from ab initio calculations using the multireference averaged coupled-pair functional (MR-ACPF) method in conjunction with the correlation-consistent core-valence basis sets up to octuple-zeta quality. The importance of several effects, including electron correlation beyond the MR-ACPF level of approximation, the scalar relativistic, adiabatic, and nonadiabatic corrections were discussed. Along with the large one-particle basis set, all of these effects were found to be crucial to attain "spectroscopic" accuracy of the theoretical predictions of vibration-rotation energy levels of NH.

Trends in Bond Dissociation Energies of Alcohols and Aldehydes Computed with Multireference Averaged Coupled-Pair Functional Theory

As part of our ongoing investigation of the combustion chemistry of oxygenated molecules using multireference correlated wave function methods, we report bond dissociation energies (BDEs) in C1-C4 alcohols (from methanol to the four isomers of butanol) and C1-C4 aldehydes (from methanal to butanal). The BDEs are calculated with a multireference averaged coupled-pair functional-based scheme. We compare these multireference BDEs with those derived from experiment and single-reference methods. Trends in BDEs for the alcohols and aldehydes are rationalized by considering geometry relaxations of dissociated radical fragments, resonance stabilization, and hyperconjugation. Lastly, we discuss the conjectured association between bond strengths and rates of hydrogen abstraction by hydroxyl radicals. In general, abstraction reaction rates are higher at sites where the C-H bond energies are lower (and vice versa). However, comparison with available rate data shows this inverse relationship between bond strengths and abstraction rates does not hold at all temperatures.

Accurate Bond Energies of Biodiesel Methyl Esters from Multireference Averaged Coupled-Pair Functional Calculations

Accurate bond dissociation energies (BDEs) are important for characterizing combustion chemistry, particularly the initial stages of pyrolysis. Here we contribute to evaluating the thermochemistry of biodiesel methyl ester molecules using ab initio BDEs derived from a multireference averaged coupled-pair functional (MRACPF2)-based scheme. Having previously validated this approach for hydrocarbons and a variety of oxygenates, herein we provide further validation for bonds within carboxylic acids and methyl esters, finding our scheme predicts BDEs within chemical accuracy (i.e., within 1 kcal/mol) for these molecules. Insights into BDE trends with ester size are then analyzed for methyl formate through methyl crotonate. We find that the carbonyl group in the ester moiety has only a local effect on BDEs. C═C double bonds in ester alkyl chains are found to increase the strengths of bonds adjacent to the double bond. An important exception are bonds beta to C═C or C═O bonds, which produce allylic-like radicals upon dissociation. The observed trends arise from different degrees of geometric relaxation and resonance stabilization in the radicals produced. We also compute BDEs in various small alkanes and alkenes as models for the long hydrocarbon chain of actual biodiesel methyl esters. We again show that allylic bonds in the alkenes are much weaker than those in the small methyl esters, indicating that hydrogen abstractions are more likely at the allylic site and even more likely at bis-allylic sites of alkyl chains due to more electrons involved in π-resonance in the latter. Lastly, we use the BDEs in small surrogates to estimate heretofore unknown BDEs in large methyl esters of biodiesel fuels.

Analysis of and remedies for unphysical ground states of the multireference averaged coupled-pair functional

A Multireference Configuration Interaction (MRCI) wavefunction includes both static and dynamic electron correlation. MRCI's well-known flaw, a lack of size extensivity, can be ameliorated with the Multireference Averaged Coupled-Pair Functional (MRACPF). However, the original MRACPF is frequently unstable, sometimes producing unphysical results. The more Multireference Averaged Quadratic Coupled-Cluster and MRACPF2 functionals also occasionally exhibit unphysical behavior. We find that these instabilities are avoided crossings with unphysical solutions to the MRACPF equations. We present two approaches to avoid the undesirable unphysical solutions.

Ab initio ground-state potential energy functions of beryllium monohydride ions: BeH+ and BeH−

The accurate ground-state potential energy functions of beryllium monohydride (BeH) cation and anion have been determined from ab initio calculations using the multi-reference averaged coupled-pair functional (MR-ACPF) method in conjunction with the correlation-consistent core-valence basis sets up to septuple-zeta quality. The effects of electron correlation beyond the MR-ACPF level of approximation, as well as the scalar relativistic and adiabatic corrections were taken into account. The vibration-rotation energy levels of the BeH, BeD, and BeT isotopologues of both ions were predicted to near "spectroscopic" accuracy. The results can be useful in a future experimental detection of the BeH anion by high-resolution vibration-rotation spectroscopy.

Approximately size extensive local multireference singles and doubles configuration interaction

Multi-reference Configuration Interaction (MRCI) is often used to predict the electronic structures and reaction energetics of small molecules with very high accuracy. Unfortunately, MRCI is inapplicable to large or even medium-sized molecules for two reasons: its computational cost scales poorly with molecule size and MRCI methods are not size extensive, leading to large energy errors. We have developed a new local (L) and approximately size extensive MRCI method that addresses both shortcomings. Truncating long-range electron correlation in a local orbital basis as well as efficient processing of two-electron integrals via Cholesky decomposition (CD) and integral screening reduce the computational cost to O(N(3)) with a small prefactor. A priori and a posteriori size extensivity corrections are both considered. The Multi-reference Averaged Coupled-Pair Functional (MRACPF) provides approximate size extensivity by modifying the energy functional. The very inexpensive Davidson-Silver and Pople a posteriori schemes also produce quite accurate corrections over a large range of molecular size. Employing CD-LMRACPF is slightly more expensive than using a Davidson-type correction, but the former gives superior results. Molecules with up to 50 heavy atoms can be treated with our CD-LMRACPF method thus far.

The ab initio ground-state potential energy function of beryllium monohydride, BeH

The accurate ground-state potential energy function of beryllium monohydride, BeH, has been determined from large-scale ab initio calculations using the multi-reference averaged coupled-pair functional (MR-ACPF) method in conjunction with the correlation-consistent core-valence basis sets up to septuple-zeta quality. The effects of electron correlation beyond the MR-ACPF level of approximation were taken into account. The scalar relativistic and adiabatic (the diagonal correction) effects, as well as some of the nonadiabatic effects, were also discussed. The vibration-rotation energy levels of three isotopologues, BeH, BeD, and BeT, were predicted to sub-cm(-1) accuracy.

Quantum chemical assessment of the binding energy of CuO+

We present a detailed theoretical investigation on the dissociation energy of CuO(+), carried out by means of coupled cluster theory, the multireference averaged coupled pair functional (MR-ACPF) approach, diffusion quantum Monte Carlo (DMC), and density functional theory (DFT). At the respective extrapolated basis set limits, most post-Hartree-Fock approaches agree within a narrow error margin on a D(e) value of 26.0 kcal mol(-1) [coupled-cluster singles and doubles level augmented by perturbative triples corrections, CCSD(T)], 25.8 kcal mol(-1) (CCSDTQ via the high accuracy extrapolated ab initio thermochemistry protocol), and 25.6 kcal mol(-1) (DMC), which is encouraging in view of the disaccording data published thus far. The configuration-interaction based MR-ACPF expansion, which includes single and double excitations only, gives a slightly lower value of 24.1 kcal mol(-1), indicating that large basis sets and triple excitation patterns are necessary ingredients for a quantitative assessment. Our best estimate for D(0) at the CCSD(T) level is 25.3 kcal mol(-1), which is somewhat lower than the latest experimental value (D(0) = 31.1 ± 2.8 kcal mol(-1)[semicolon] reported by the Armentrout group) [Int. J. Mass Spectrom. 182/183, 99 (1999)]. These highly correlated methods are, however, computationally very demanding, and the results are therefore supplemented with those of more affordable DFT calculations. If used in combination with moderately-sized basis sets, the M05 and M06 hybrid functionals turn out to be promising candidates for studies on much larger systems containing a [CuO](+) core.

F + H2 → FH + H potential energy surface: Construction of the reference configuration state function space and MR‐ACPF‐2 results

AbstractA new electronic configuration reference space (subsequently used in multi‐reference averaged coupled pair functional (MR‐ACPF) or multi‐reference configuration interaction singles and doubles [MR‐CI(SD)] level treatments of electron correlation) is determined using the aug‐cc‐pVQZ basis set as a step toward constructing a new potential energy surface (PES) for the F + H2 → FH + H reaction. We use our new reference space to calculate several chemically important properties (e.g., barriers, exothermicity, van der Waals wells) of the F + H2 PES. We obtain nonrelativistic barrier heights of 1.32 kcal/mol−1 (bent) and 1.67 kcal/mol−1 (collinear) that are ∼0.2–0.3 kcal/mol−1 lower than those obtained from the current best PES. Our nonrelativistic value for the exothermicity is 32.45 kcal/mol−1, which is 0.7–1.1 kcal/mol−1 higher than the values obtained from some other PESs and 0.45 kcal/mol−1 higher than the experimental value. The van der Waals wells we find are slightly deeper (0.05 kcal/mol−1) than the wells on the other PES. The ≈1‐kcal/mol−1 magnitude of the differences among barrier heights, exothermicities, and well depths, obtained in our work and using the most reliable current PESs suggest that to obtain a three‐dimensional (3D) PES for the F + H2 → FH + H accurate to 0.2 kcal/mol−1, we will have to use even higher‐level methods (e.g., explicitly correlated wave functions) and include relativistic corrections. We intend to do so in the next phase of this effort that is currently under way. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Electronic ground states of the V2O4+/0/- species from multireference correlation and density functional studies.

The molecular and electronic structures of the V2O4+/0/- species are examined by multireference averaged coupled-pair functional (MR-ACPF) and density functional B3LYP calculations. For all three species, new conformers have been found. Shallow potential energy curves imply high mobility of the oxygen atoms in the neutral and anionic species for which antiferromagnetic coupling of the weakly interacting 3dV electrons is found. Good agreement between the MR-ACPF and B3LYP results for the molecular structures and the relative energies of states with different spin multiplicity, as well as for the ionization energy and electron affinity, is observed. For the computation of the height of the transition barriers between different conformers elaborated MR-ACPF calculations are required.

The performance of the multireference Brillouin–Wigner coupled cluster singles and doubles method on the insertion of Be into H 2

The perpendicular (C 2v) insertion pathway of (X 1S) Be into (X 1 Σ g + ) H 2 is calculated by means of the multireference Brillouin–Wigner coupled cluster singles and doubles (MRBWCCSD) method and compared with the results of full configuration interaction (FCI), the multireference averaged coupled pair functional (MRACPF), and with previously reported MRCCSD results. MRBWCCSD is shown to provide a fairly accurate description of the BeH 2 potential energy surface. If higher accuracy is required, inclusion of connected triples into the MRCC model seems to be unavoidable.

Excitation energies and transition moments by the multireference averaged quadratic coupled cluster (MR-AQCC) method

The MR-AQCC (multireference averaged quadratic coupled cluster) and the MR-ACPF (multireference averaged coupled pair functional) methods can be considered as size-extensivity corrected MR-CISD procedures. So far, they have been applied mostly to ground state calculations of a given symmetry. By formulating MR-AQCC and MR-ACPF in terms of a diagonal shift to the Hamiltonian this restriction is removed. In order to compute transition moments, linear response theory (LRT) is used since there is no wavefunction defined within these methods. A LRT-compliant variant of MR-AQCC and MR-ACPF is developed which allows a consistent formulation of transition energies and moments. In calculations on CH2, CH+ and C2 (where full CI results are available) it is shown that MR-AQCC brings about a substantial improvement for excitation energies and transition moments as compared to MR-CISD.

Bond Strengthening by Deformation of Bond Angles

Torsion potentials about the X−ẌH bond in homosubstituted primary carbenes (X = C) and silylenes (X = Si) have been investigated at the multireference averaged coupled pair functional (MRACPF) level of theory. For the triplet species, the potentials are quite flat, but large barriers of torsion have been observed for the singlet states of all carbenes and silylenes whose carbon or silicon atom adjacent to the divalent atom formes small bond angles with two of its further substitutents; other geometry parameters, even the bond angle at the divalent atom, proved to be of little or no importance. The said kind of deformation encourages the formation of a weak dative π-like bond between the two X atoms, which by its 2-fold symmetry with respect to torsion about the bond axis is responsible for the observed two-minima torsion potential.

Energy-adjusted pseudopotentials for the actinides. Parameter sets and test calculations for thorium and thorium monoxide

We present nonrelativistic and quasirelativistic energy-adjusted pseudopotentials, the latter augmented by spin–orbit operators, as well as optimized (12s11p10d8f)/ [8s7p6d4f]-Gaussian-type orbitals (GTO) valence basis sets for the actinide elements actinium through lawrencium. Atomic excitation and ionization energies obtained by the use of these pseudopotentials and basis sets in self-consistent field (SCF) calculations differ by less than 0.2 eV from corresponding finite-difference all-electron results. Large-scale multiconfiguration self-consistent field (MCSCF), multireference configuration interaction (MRCI), and multireference averaged coupled-pair functional (MRACPF) calculations for thorium and thorium monoxide yield results in satisfactory agreement with available experimental data. Preliminary results from spin–orbit configuration interaction calculations for the low-lying electronic states of thorium monoxide are also reported.

The photodissociation of ClNO through excitation in the T1 state: An ab initio study

An ab initio study of the photodissociation of ClNO following excitation of the T1 state is presented. The corresponding three-dimensional potential-energy surface has been calculated using extensive complete-active-space self-consistent-field (CASSCF) and multireference-averaged coupled pair functional (MR-ACPF) wave functions and large basis sets. The nuclear dynamics has been treated by solving the time-dependent Schrödinger equation in three dimensions. The steepness of the potential with respect to the dissociation coordinate in the Franck–Condon region is found to be very crucial for a realistic description of the dissociation dynamics. It controls directly the lifetime of the ClNO(T1) complex and therefore the widths of the vibrational structures in the absorption spectrum. Due to very large dynamical electron correlation effects, the CASSCF potential is found to be much too steep. Even with extended MR-ACPF wave functions an empirical scaling of the correlation energy is necessary in order to obtain a potential which is sufficiently flat in the transition region to allow for the splitting of each vibrational band into three bending peaks. Only the absorption spectrum calculated with the scaled MR-ACPF potential is in very good agreement with the measured spectrum. The dissociation proceeds adiabatically as far as the vibrational degree of freedom of NO is concerned with the result that excitation of ClNO(T1) within vibrational band n* yields almost exclusively products NO(n*). The degree of rotational excitation of the NO fragment is relatively low, i.e., the distributions peak at low rotational quantum numbers. The calculations reproduce the intriguing relation between the bending state in the ClNO(T1) complex (k*) and the multimodal structures in the final rotational-state distributions, first observed experimentally by Reisler and co-workers [J. Chem. Phys. 89, 6547 (1988)].

A theoretical study of the complexes of N2O with H+, Li+, and HF using various correlation methods

Binding energies for complexes of N2O with the acids H+, Li+, and HF have been computed using the following correlation methods: many-body (Moller–Plesset) perturbation theory at second (MP2), third (MP3), and fourth (MP4) order; the “quadratic CI” method with single and double excitations (QCISD) and with noniterative inclusion of triple excitations (QCISD(T)); the linearized coupled-cluster method (LCCM); the averaged coupled-pair functional (ACPF); configuration interaction with all single and double excitations (CISD); and CISD with the Davidson and Pople corrections. The convergence of the Moller–Plesset expansion is erratic, predicting that the terminal nitrogen is the preferred binding site for the complexes at the MP2 and MP4 levels, in disagreement with Hartree–Fock and MP3 and all other models (including the infinite-order QCI). The effect of triple excitations at MP4 and QCI is to destabilize complexes bound at O and stabilize those bound at N, but this effect is greatly overestimated at MP4 relative to QCI. Except for the LCCM result for N-protonated N2O, ACPF and LCCM bindin energies are similar to the QCISD values. The size-consistency error in the ACPF binding energies of the complexes of N2O with HF is about 0.5 kcal/mol. The CISD size-consistency error for these complexes is 23 kcal/mol, leading to negative binding energies when computed relative to isolated N2O and HF. The Davidson correction reduces the size-consistency error but still leaves the binding energies negative. The Pople correction produces positive but too small binding energies. However, all methods give consistenly good, essentially indistinguishable binding energies when computed relative to a similar calculation on a supermolecule of infinitely separated N2O and HF units. Multireference ACPF and CISD binding energies have also been obtained using MCSCF reference functions which correlate the highest occupied and lowest virtual pairs of π orbitals. The multireference binding energies are not greatly different from the single-reference values, and do not reverse the negative binding energies of the complexes with HF at the CISD level when computed relative to isolated molecules. When calculated relative to the infinitely separated supermolecule, the multireference binding energies of these complexes are virtually identical to the corresponding single-reference values.