Averaged Coupled-pair Functional Research Articles

The electronic spectrum of AgI2. Ab initio benchmark CASSCF + Averaged Coupled Pair Functional studies on the ligand-field states including spin-orbit couplings

The X2Πg, 2Σg+ and 2Δg states of AgI2 have been studied through benchmark ab initio CASSCF + Averaged Coupled Pair Functional (ACPF) calculations using especially developed valence basis sets to study the transition energies and equilibrium geometries. The spin–orbit (SO) effects were included through the effective Hamiltonian formalism using the |ΛSΣ〉 ACPF energies as diagonal elements. AgI2 is a linear centrosymmetric molecule with a 2Πg ground state, in contradiction with ligand-field theory. The ACPF adiabatic excitation energies of the 2Σg+ and 2Δg states are 7344 and 26085 cm−1, respectively. A comparison of the present results with the previous ones for AgCl2 and AgBr2 shows a monotonic increase in the 2Πg-2Σg+ and 2Πg-2Δg transition energies due to a decrease of the ionic structures in the LF states as the atomic number of the halogen grows. The inclusion of the SO effects leads to a pure Ω = 3/2 X(2Πg) ground state, a Ω = 1/2 (83% 2Πg + 17% 2Σg+) A state, a Ω = 1/2 (17% 2Πg + 83% 2Σg+) B state, a Ω = 5/2 (2Δg) C state and a Ω = 3/2 (2Δg) D state. The X-A, X-B, X-C, X-D vertical transition energies are 4250, 11248, 27,127 and 30441 cm−1, respectively, nearly identical to the adiabatic Te values.

Electric dipole moment function and line intensities for the ground state of carbon monxide**Project supported by the National Natural Science Foundation of China (Grant Nos. 11374217 and 11474207).

An accurate electric dipole moment function (EDMF) is obtained for the carbon monoxide (CO) molecule (X1Σ+) by fitting the experimental rovibrational transitional moments. Additionally, an accurate ab initio EDMF is found using the highly accurate, multi-reference averaged coupled-pair functional (ACPF) approach with the basis set, aug-cc-pV6Z, and a finite-field with ±0.005 a.u. (The unit a.u. is the abbreviation of atomic unit). This ab initio EDMF is very consistent with the fitted ones. The vibrational transition matrix moments and the Herman–Wallis factors, calculated with the Rydberg–Klein–Rees (RKR) potential and the fitted and ab initio EDMFs, are compared with experimental measurements. The consistency of these line intensities with the high-resolution transmission (HITRAN) molecular database demonstrates the improved accuracy of the fitted and ab initio EDMFs derived in this work.

A Parametrized Coupled-Pair Functional for Molecular Interactions: PCPF-MI.

We present a parametrized coupled-pair functional, optimized to describe molecular interactions (PCPF-MI). The method has the same computational cost as singles and doubles configuration interaction, is size extensive, and yields energies that are stationary with respect to variations in all of its excitation coefficients. This last property facilitates the construction of density matrices and the evaluation of one- and two-electron properties. For the S22, HSG, S66, and A24 databases of van der Waals dimers, PCPF-MI computations yield interaction energies with mean unsigned errors of 0.326, 0.149, 0.214, and 0.044 kcal mol(-1), respectively, relative to benchmark computations. PCPF-MI interaction energies consistently improve upon those obtained from several other coupled-pair methods, including the averaged coupled-pair functional (ACPF), the coupled electron-pair approximation [CEPA(n), n = 0,1,3], and averaged quadratic coupled cluster (AQCC). Optimal parameters for spin-component-scaled (SCS) variants of each of these methods are also presented. SCS-CEPA(0), SCS-CEPA(1), SCS-ACPF, and SCS-PCPF-MI all perform similarly, with average errors for the four databases of roughly 0.1 kcal mol(-1). The PCPF-MI method, without additional SCS parametrization, has an average error of 0.192 kcal mol(-1) over the four databases and, when compared to the SCS-parametrized coupled-pair methods, has the added benefit that the energy is stationary with respect to variations in all its excitation coefficients.

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.

The electronic spectrum of AgBr2: Ab initio benchmark calculations on the 2Πu and 2Σu+ charge transfer states including spin‐orbit effects

AbstractThe 2Πu and 2Σu+ charge transfer (CT) states of AgBr2 have been studied through benchmark ab initio HF, complete active space SCF, CASPT2, NEVPT2, and averaged coupled pair functional (ACPF) multireference calculations using especially developed valence basis sets to study the transition energies, geometries, vibrational frequencies, and Mulliken charges. The spin‐orbit (SO) effects have been included through the effective Hamiltonian formalism using the ACPF energies as |ΛSΣ> diagonal elements. The equilibrium Ag–Br distance for both CT states is larger than that of the X2Πg ground state. The ACPF adiabatic excitation energies of the 2Πu and 2Σu+ states are 4620 and 7006 cm‐1, respectively. Using previous ACPF benchmark studies showing that the 2Δg ligand field (LF) state lies more than 20,000 cm‐1 above the ground state, these new results lead to the following energetic ordering for the five lowest electronic states of AgBr2: X2Πg, 2Σg+, 2Πu, 2Σu+, and 2Δg, in sharp contradiction with Hartree–Fock theory. When considering the coupling of the LF and CT states, the inclusion of the SO effects leads to a pure Ω = 3/2 (X2Πg) ground state, Ω = 1/2 (92% 2Πg + 8% 2Σg+) A state, Ω = 3/2 (pure 2Πu) B state, Ω = 1/2 (68% 2Πu+32% 2Σu+) C state, Ω = 1/2 (8% 2Πg + 92% 2Σg+) D state, and an Ω = 1/2 (32% 2Πu + 68% 2Σu+) E state. We present here what we consider the most complete and accurate account of the electronic spectrum of AgBr2. © 2012 Wiley Periodicals, Inc.

ChemInform Abstract: Binding Energies and Bond Distances of Ni(CO)x, x = 1-4: An Application of Coupled-Cluster Theory.

The accuracy of the single and double excitation coupled‐cluster (CCSD) method that includes a perturbational estimate of connected triple excitations, denoted CCSD(T), has been tested for some representative transition metal complexes. For both the binding energy and metal to ligand bond distance of NiCO and Ni(CO)2, the CCSD(T) method yields results in very good agreement with multireference averaged coupled‐pair functional (ACPF) calculations. The results are much better than those obtained using either the coupled‐pair functional (CPF) or modified CPF (MCPF) methods. The contribution of connected triples to the binding energy is significant for all Ni(CO)x, x=1–4 ranging from 15 kcal/mol for NiCO to 30 kcal/mol for Ni(CO)4. In contrast, for the geometries the connected triples are only of minor importance. In this case, the correct treatment of disconnected quadruple excitations appears to be more important. For Ni(CO)4, the calculated binding energy is 125 kcal/mol (expt. 140 kcal/mol) and the bond d...

The electronic spectrum of AgBr 2: Ab initio benchmark vs. DFT calculations on the lowest ligand-field states including spin–orbit effects

The X 2Π g, 2Σ g + and 2Δ g states of AgBr 2 have been studied through benchmark ab initio CASSCF + Averaged Coupled Pair Functional (ACPF) and DFT calculations using especially developed valence basis sets to study the transition energies, geometries, vibrational frequencies, Mulliken charges and spin densities. The spin–orbit (SO) effects were included through the effective hamiltonian formalism using the |ΛSΣ〉 ACPF energies as diagonal elements. At the ACPF level, the ground state is 2Π g, in contradiction with ligand-field theory and Hartree–Fock results. The ACPF adiabatic excitation energies of the 2Σ g + and 2Δ g states are 3825 and 20 152 cm −1, respectively. The inclusion of the SO effects leads to a pure Ω = 3/2 ( 2Π g) ground state, a Ω = 1/2 (97% 2Π g + 3% 2Σ g +) A state, a Ω = 1/2 (3% 2Π g + 97% 2Σ g +) B state, a Ω = 5/2 ( 2Δ g) C state and a Ω = 3/2 (99% 2Δ g) D state. The B97, B3LYP and PBE0 functionals, which were shown to yield accurate transition energies for CuCl 2, overestimate the X 2Π g– 2Σ g + T e by around 25% but provide a qualitative energetic ordering in agreement with CASSCF and ACPF results. The nature of the bonding in the X 2Π g ground state is different from that of AgCl 2 since the Mulliken charge on the metal is 0.95 while the spin density is only 0.39. DFT strongly delocalizes the spin density providing even smaller values of around 0.13 on Ag not only for the ground state, but also for the 2Σ g + state.

Ability of a coupled electron pair approximation to treat single bond breakings

The self-consistent size-consistent CI ((SC) 2CI), which considers all exclusion principle violating (EPV) diagrams, is able to treat single bond breakings, despite its single-reference character. It is shown here that a CEPA-3 (coupled electron pair approximation) dressing, considering only the EPVs through the occupied molecular orbitals, treats satisfactorily the single bond breaking processes, while the uniform dressings, e.g. CEPA-0, the averaged coupled pair functional (ACPF) or averaged quadratic coupled cluster (AQCC) lead to non-convergence or spurious energy lowering in such processes. A number of test calculations illustrate this rationalizable feature.

Multireference averaged quadratic coupled-cluster (MR-AQCC) method based on the functional of the total energy

In this short paper a new version of the multireference (MR) averaged coupled pair functional (ACPF) and the MR averaged quadratic coupled-cluster (AQCC) methods is presented which corrects the failure of the original formulation in case of close-lying states described with small reference space. This new version is based on a functional which also includes the reference energy, i.e. instead of optimizing the correlation energy, the total energy will be made stationary with respect the wave function parameters. It is demonstrated that this method gives smooth potential energy surfaces in case of avoided crossings.

Ab initio studies on the electronic structure of FeOH

The electronic structure of FeOH has been studied by using the all-electron multireference averaged coupled-pair functional (ACPF) method combined with the scalar-relativistic Douglas–Kroll–Heβ (DKH) Hamiltonian. A linear geometry (ground state 6Δ, RFe–O = 1.7501 Å, RO–H = 0.9444 Å) is found to be the most stable structure for FeOH. Relativistic effects must be taken into account in order to predict the correct ground state. Furthermore, inner-shell correlation effects are also important for the Fe–O bond of FeOH, i.e., the Fe–O distance is lengthened by at least 0.02 Å when the iron 3s and 3p orbitals are frozen at the ACPF level. The calculated ionization energy IE (7.43 eV) and standard gas phase enthalpies of formation ΔHf0 (21.03 kcal/mol) are in good agreement with Gorokhov’s measurement (IE: 7.6 ± 0.3 eV, ΔHf0 : 25.4 ± 4.1 kcal/mol). The obtained Fe–OH dissociation energy D0 (3.61 eV) agrees well with the recent experimental value 3.50 ± 0.12 eV obtained by Schröder and Schwarz but exceeds the error bar of Murad’s older measurement (3.33 ± 0.17 eV ) by 0.13 eV.

Size extensive modification of local multireference configuration interaction.

We recently developed a reduced scaling multireference configuration interaction (MRCI) method based on local correlation in the internal (occupied) and external (virtual) orbital spaces. This technique can be used, e.g., to predict bond dissociation energies in large molecules with reasonable accuracy. However, the inherent lack of size extensivity of truncated CI is a disadvantage that in principle worsens as the system size grows. Here we implement an a priori size-extensive modification of local MRCI known as the averaged coupled pair functional (ACPF) method. We demonstrate that local MR-ACPF recovers more correlation energy than local MRCI, in keeping with trends observed previously for nonlocal ACPF. We test the size extensivity of local ACPF on noninteracting He atoms and a series of hydrocarbons. Basis set and core correlation effects are explored, as well as bond breaking in a variety of organic molecules. The local MR-ACPF method proves to be a useful tool for investigating large molecules and represents a further improvement in predictive accuracy over local MRCI.

The performance of multi-reference ACPF-like methods for the dipole moment of FeO

We compare the performance of the multi-reference formulations of averaged coupled-pair functional (ACPF), averaged quadratic coupled-cluster (AQCC), and the novel ACPF-2, together with configuration interaction, CI(SD), on the difficult case of the dipole moment of FeO. AQCC and ACPF-2 give the same results and the stability of these two methods is dramatically better than that of ACPF. Since ACPF-2 is generally close to ACPF when the zeroth-order wavefunction, Ψ 0, is good approximation to the total wavefunction, ACPF-2 combines the favorable features of AQCC (stability) and of ACPF (accuracy) without having the drawbacks of these latter two methods. Thus, regardless on the quality of Ψ 0, the novel ACPF-2 is the method to be preferred among the ACPF-like functionals.

A Theoretical Study of MgNC and MgCN in the X̃2Σ + Electronic State

The MgNC radical was the first Mg-containing species to be observed in interstellar space. This fact has stimulated considerable spectroscopic interest in this molecule, and in its isomer MgCN, but nevertheless the only rotationally resolved spectroscopic data presently available for X̃ 2Σ + MgNC comprise the rotational spectrum (K. Kawaguchi et al., 1993, Astrophys. J. 406, L39–L42; K. Ishii et al., 1993, Astrophys. J. 410, L43–L44; M. A. Anderson and L. M. Ziurys, 1994, Chem. Phys. Lett. 231, 164–170; E. Kagi et al., 1996, J. Chem. Phys. 104, 1263–1267; E. Kagi and K. Kawaguchi, J. Mol. Spectrosc. 2000, 199, 309–310) together with a few vibronic bands, all originating in the vibronic ground state and belonging to the à 2Π← X̃ 2Σ + electronic transition (R. R. Wright and T. A. Miller, 1999, J. Mol. Spectrosc. 194, 219–228). For MgCN, only the rotational spectrum in the vibrational ground state is known (M. A. Anderson, T. C. Steimle, and L. M. Ziurys, 1994, Astrophys. J. 429, L41–L44). We report here potential energy surfaces calculated by the Averaged Coupled-Pair Functional (ACPF) method with TZ3P+f (Mg), TZ2P+f(N,C) basis sets including core-valence correlation due to the Mg 2s and 2p electrons. The ab initio results are used for determining the standard spectroscopic constants of X̃ 2Σ + MgNC and MgCN. Also, we report variational calculations of the rotation–vibration energies, and variational simulations of the lowest rotation–vibration bands, carried out with the MORBID program system (P. Jensen, 1988, J. Mol. Spectrosc. 128, 478–501). We hope that our theoretical results will encourage and facilitate further characterization of X̃ 2Σ + MgNC and MgCN by high-resolution spectroscopy.

A new version of the multireference averaged coupled‐pair functional (MR‐ACPF‐2)

AbstractThe averaged coupled‐pair functional (ACPF), as found in R. J. Gdanitz and R. Ahlrichs, Chem. Phys. Lett. 143 (1988), is probably the most successful method to approximate full configuration interaction (CI) on the multireference (MR) level of theory. However, ACPF has a tendency to slightly overestimate the effect of higher than double substitutions, which, when the zeroth‐order wavefunction is of poor quality, may deteriorate the accuracy or even create instabilities. Since the properties of the ACPF and similar methods have apparently not always been correctly described in the literature, we repeat the derivation of this method in some detail. We analyze the connection between the (original) ACPF and the similar averaged quadratic coupled cluster (AQCC) method (which may be regarded as a damped ACPF), on one hand, and the different versions (0–3) of the coupled electron‐pair approximation (CEPA), on the other hand. We find that ACPF and AQCC may be regarded as CEPA‐1, respectively, CEPA‐3, where the shifts of the Hamiltonian are substituted by a single averaged shift. As CEPA‐3 considerably underestimates correlation effects, AQCC shows the same behavior. However, when the zeroth‐order wavefunction is of poor quality, AQCC may be more stable and thus more accurate than ACPF. By analyzing the role of the single substitutions, we find that ACPF may especially overestimate their contribution to unlinked clusters like \documentclass{article}\pagestyle{empty}\begin{document}$\textstyle\frac{1}{2}\hat{T}^{2}_{1}$\end{document}. We therefore propose a new version, called ACPF‐2, where (in contrast to AQCC) only the renormalization factor, g, that corresponds to the singles, is damped; i.e., we have (4/N)[1−1/(2N−2)]. In the limit of a large number of electrons, N, this factor becomes two times as large as in the (original) ACPF, where 2/N is used. In order to test the new ACPF‐2 method, we perform numerous comparisons with full CI, as well as calculations including terms that are linear in the interelectronic distances, rij. We find that in difficult cases, ACPF‐2 is of similar stability as is AQCC and is thus considerably more accurate than the original ACPF. In contrast to AQCC, however, ACPF‐2 achieves this stability without sacrificing the high accuracy which is obtained by ACPF in well‐behaved cases. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

Ab initio model potential embedded-cluster study of the ground and lowest excited states of Cr3+ defects in the elpasolites Cs2NaYCl6 and Cs2NaYBr6

In this paper we present the results of an ab initio model potential (AIMP) embedded-cluster study of the ground and lowest excited states of Cr3+ defects in the elpasolites Cs2NaYCl6 and Cs2NaYBr6; complete active space SCF (CASSCF) and averaged coupled-pair functional (ACPF) calculations are performed on CrCl63− and CrBr63− clusters embedded in ab initio model potential representations of the surrounding lattices Cs2NaYCl6 and Cs2NaYBr6. The experimental structural data are revisited and some new results are found which differ significantly from those available in the literature. The calculated local structure parameters and electronic transition energies which can be compared to experiments are found to be very good; new structural and spectroscopic results are produced which have been neither measured nor calculated, which are complementary to the available ones, and whose quality is expected to be high as well. In particular, the question of the competition of the excited-state absorptions with the potential vibronic laser emission has been adressed: A considerable overlap between the broad Eg2→A1g2 excited-state absorption and A2g4←4 T2g emission bands is predicted in both materials, which must result in a reduction in the emission efficiency. Finally, it is shown that the quantum mechanical embedding effects due to the fact that the external Cs+, Na+, Y3+, Cl−, and Br− ions are not point charges, are non-negligible; lacking of these effects must be one of the reasons which make previous Density Functional Theory calculations show significantly larger discrepancies with the available experiments.

Computational Thermochemistry of Medium-Sized Silicon Hydrides

Standard enthalpies ΔfH298, entropies S298, and Gibbs functions of formation ΔfG298 for a large number of silicon hydrides containing one to five Si atoms have been calculated. The choice of compounds includes cyclic and acyclic silanes, silyl radicals, silylenes, disilenes, and cyclic diradicals. The thermodynamic functions were calculated using an empirically corrected ab initio scheme. The electronic energies were obtained with multiconfiguration reference averaged coupled-pair functional (ACPF) wave functions. Two different basis sets were employed to demonstrate the validity of the correction scheme. The computed data are compared with experimental and theoretical data from other laboratories. Increment rules and substituent effects are presented and various reaction enthalpies are tabulated and discussed. The performance of the correction scheme and potential pitfalls in its general applicability are discussed.

Redox Properties of the Diatomic Bare Iron Chalcogenides FeO and FeS in the Gas Phase

AbstractThe electron‐transfer behavior of the binary iron chalcogenides FeO and FeS has been examined by means of mass spectrometry and ab initio calculations using the averaged coupled‐pair functional (ACPF) method. The experimental and theoretical results are in good agreement with each other and also with previous studies. The ionization energies (IE) of the diatomic species are found to be IE(FeO) = 8.8±0.2 eV, IE(FeO+) = 17.9±0.4 eV, IE(FeS) = 8.3±0.3 eV, and IE(FeS+) = 16.3±0.5 eV. Two new diatomic dications, FeS2+ and FeO2+, are shown to exist as metastable minima on the corresponding potential‐energy surfaces. The data enable an evaluation of the intrinsic gas‐phase redox properties of FeS and FeO, and the comparison demonstrates that iron sulfide is more prone to undergo facile reduction and oxidation than iron oxide.

Momentum profiles for open shell molecules: studies of the HOMOs of NO, O2 and NO2 by electron momentum spectroscopy and SCF, post-Hartree-Fock and DFT calculations

Measurements of the outermost valence electron orbital momentum profiles of the open shell molecules NO, O2 and NO2 have been obtained using electron momentum spectroscopy (EMS). The presently reported experimental momentum profiles of NO and O2 display much improved statistics compared with previously published EMS results while the data for the HOMO of NO2 is the first reported. In the case of NO, the present measurements are considerably different from previous results and these differences appear to be due to the presence of NO2 impurities in the previous work. The EMS measurements provide a stringent test of basis set effects and the quality of ab initio methods in the description of these open shell systems. The experimental momentum profiles have been compared with theoretical spherically averaged momentum profiles from several basis sets calculated at the level of the target Hartree-Fock approximation (THFA) with a range of basis sets using both unrestricted Hartree-Fock (UHF) and restricted open shell Hartree-Fock (ROHF) methods. Various configuration interaction calculations such as multi-reference singles and doubles configuration interaction (MRSD-CI), averaged coupled pair functional (ACPF) and quasi-degenerate variational perturbation theory (QDVPT) calculations of the full ion-neutral overlap amplitude have also been compared to experiment to investigate the effects of electron correlation and relaxation. The experimental momentum profiles have further been compared to calculations at the level of the target Kohn-Sham approximation (TKSA) using density functional theory (DFT) with the local density approximation and also with gradient corrected exchange-correlation potentials. In addition to momentum profiles, other electronic properties such as total energies, dipole moments, quadrupole moments and values of the electronic spatial extent have been calculated by the various theoretical methods and compared to experimental values.