Fock space multi-reference coupled-cluster method for energies and energy derivatives

Fock Space Coupled-Cluster Method for the Ground and Excited States of the NaMg+ Molecular Cation

This study presents a theoretical investigation of the potential energy curves (PECs) and spectroscopic constants of the NaMg+ molecular cation using the intermediate Hamiltonian Fock space coupled-cluster method with singles and doubles within the (2,0) sector [IH-FS-CCSD(2,0)]. The NaMg+ cation has gained scientific interest due to its potential applications in ultracold chemistry, yet it remains experimentally unexplored. We computed 20 lowest-lying PECs and assigned them to 10 dissociation limits. Our results demonstrated high accuracy, and computed curves are smooth and continuous over the entire range of interatomic distances. The study validates the effectiveness of the IH-FS-CCSD(2,0) method in describing PECs of diatomic molecular cations composed of alkali and alkaline earth metals and provides a solid theoretical foundation for further studies of NaMg+ and similar systems.

Intermediate Hamiltonian Fock-space coupled-cluster theory for excitation energies, double ionization potentials, and double electron attachments with spin–orbit coupling

The intermediate Hamiltonian Fock-space coupled-cluster methods at the singles and doubles level (IHFSCCSD) for excitation energies in the (1p, 1h) sector, double ionization potentials in the (0p, 2h) sector, and double electron attachments in the (2p, 0h) sector of the Fock space are implemented based on the CCSD method with spin–orbit coupling (SOC) included in the post-Hartree–Fock treatment using a closed-shell reference in this work. The active space is chosen to contain those orbitals that have the largest contribution to principal ionized or electron-attached states obtained from the equation-of-motion coupled-cluster calculations. Both time-reversal symmetry and spatial symmetry are exploited in the implementation. Our results show that the accuracy of IHFSCCSD results is closely related to the active space, and the sufficiency of the active space can be assessed from the percentage of transitions within the active space. In addition, unreasonable results may be encountered when the ionized or electron-attached states with a somewhat larger contribution from double excitations are included to determine the active space and cluster operators in the (0p, 1h) or (1p, 0h) sector of the Fock space. A larger active space may be required to describe SO splitting reliably than that in the scalar-relativistic calculations in some cases. The IHFSCCSD method with SOC developed in this work can provide reliable results for heavy-element systems when a sufficient active space built upon the principal ionization potential/electron affinity states is adopted.

Three-Body Excitations in Fock-Space Coupled-Cluster: Fourth Order Perturbation Correction to Electron Affinity and Its Relation to Bondonic Formalism

In this paper, we present a formulation of highly correlated Fock-space multi-reference coupled-cluster (FSMRCC) methods, including approximate triples on top of the FSMRCC with singles and doubles, which correct the electron affinities by at least at third and up to the fourth order in perturbation. We discuss various partial fourth-order schemes, which are reliable and yet computationally more efficient than the full fourth-order triples scheme. The third-order scheme is called MRCCSD+T^*(3). We present two approximate fourth-order schemes, MRCCSD+T^*−a(4) and MRCCSD+T^*(4). The results that are presented allow one to choose an appropriate fourth-order scheme, which is less expensive and right for the problem. All these schemes are based on the effective Hamiltonian scheme, and provide a direct calculation of the vertical electron affinities. We apply these schemes to a prototype Li₂ molecule, using four different basis sets, as well as BeO and CH⁺. We have calculated the vertical electron affinities of Li₂ at the geometry of the neutral Li₂ molecule. We also present the vertical ionization potentials of the Li₂ anion at the geometry of the anion ground state. We have also shown how to calculate adiabatic electron affinity, though in that case we lose the advantages of direct calculation. BeO has been examined in two basis sets. For CH⁺, four different basis sets have been used. We have presented the partial fourth-order schemes to the EA in all the basis sets. The results are analyzed to illustrate the importance of triples, as well as highlight computationally efficient partial fourth-order schemes. The choice of the basis set on the electron affinity calculation is also emphasized. Comparisons with available experimental and theoretical results are presented. The general fourth-order schemes, which are conceptually equivalent with the Fock-space multi-reference coupled-cluster singles, doubles, and triplets (MRCCSD+T) methods, based on bondonic formalism, are also presented here in a composed way, for quantum electronic affinity.

A Fock space coupled cluster based probing of the single- and double-ionization profiles for the poly-cyclic aromatic hydrocarbons and conjugated polyenes

Sequential formation of a poly-cyclic aromatic hydrocarbon (PAH) dication in the H I regions of the interstellar medium (ISM) is proposed to be a function of internal energy of the doubly ionized PAHs, which, in turn, is dependent on the single- and double-ionization potentials of the system. This sets a limit on the single- and double-ionization energies of the system(s) that can further undergo sequential absorption of two photons, leading to a dication (PAH⁺²). Here, we report the single-ionization (I⁺¹) and double-ionization (I⁺²) energies and the I⁺²/I⁺¹ ratio for some selected PAHs and conjugated polyenes obtained using the Fock space coupled cluster technique, enabling simultaneous consideration of several electronic states of different characters. The I⁺² to I⁺¹ ratio bears a constant ratio, giving allowance to determine I⁺² from the knowledge of single-ionization (I⁺¹) and vice versa. Our observations are in good agreement with the established literature findings, confirming the reliability of our estimates. The measured single- and double-ionization energies further demonstrate that the sequential formation and fragmentation of a PAH dication in the H I regions of the ISM for systems such as benzene and conjugated polyenes such as ethylene and butadiene are quite unlikely because I⁺²-I⁺¹ for such system(s) is higher than the available photon energy in the H I regions of the ISM. Present findings may be useful to understand the formation and underlying decay mechanisms of multiply charged ions from PAHs and related compounds that may accentuate the exploration of the phenomenon of high-temperature superconductivity.

Electronic states of NaLi molecule: Benchmark results with Fock space coupled cluster approach

Accurate potential energy curves (PECs) are obtained for 20 lowest lying electronic states of the NaLi molecule. The computational scheme used here is based on the multireference coupled cluster theory formulated in the (2,0) sector of the Fock space. The latter sector provides the description of states obtained by attachment of two electrons to the reference system. This makes it possible to adopt the doubly ionized NaLi⁺² molecule as a Fermi vacuum. The latter has a very concrete advantage in calculations of the PECs since it dissociates into closed shell fragments (NaLi⁺² → Na⁺ + Li⁺); hence, the restricted Hartree-Fock method can be used within the whole range of interatomic distances. Computed PECs and spectroscopic constants stay very close to the experimental values (if the latter are available) with the accuracy exceeding the other theoretical approaches including those based on the effective core polarization potentials. Relativistic corrections included at the infinite-order two-component level have a non-negligible effect on the accuracy of computed excitation and dissociation energies with contributions up to 50 cm^-1.

Negative Ion Resonance States: The Fock-Space Coupled-Cluster Way

The negative ion resonance states, which are electron-molecule metastable compound states, play the most important role in free-electron controlled molecular reactions and low-energy free-electron-induced DNA damage. Their electronic structure is often only poorly described but crucial to an understanding of their reaction dynamics. One of the most important challenges to current electronic structure theory is the computation of negative ion resonance states. As a major step forward, coupled-cluster theories, which are well-known for their ability to produce the best approximate bound state electronic eigen solutions, are upgraded to offer the most accurate and effective approximations for negative ion resonance states. The existing Fock-space coupled-cluster (FSCC) and the equation-of-motion coupled-cluster (EOM-CC) approaches that compute bound states are redesigned for the direct and simultaneous determination of both the kinetic energy of the free electron at which the electron-molecule compound states are resonantly formed and the corresponding autodetachment decay rate of the electron from the metastable compound state. This Feature Article reviews the computation of negative ion resonances using the FSCC approach and, in passing, provides the highlights of the equivalent EOM-CC approach.

Finite-Field Calculations of Transition Properties by the Fock Space Relativistic Coupled Cluster Method: Transitions between Different Fock Space Sectors

Reliable information on transition matrix elements of various property operators between molecular electronic states is of crucial importance for predicting spectroscopic, electric, magnetic and radiative properties of molecules. The finite-field technique is a simple and rather accurate tool for evaluating transition matrix elements of first-order properties in the frames of the Fock space relativistic coupled cluster approach. We formulate and discuss the extension of this technique to the case of transitions between the electronic states associated with different sectors of the Fock space. Pilot applications to the evaluation of transition dipole moments between the closed-shell-like states (vacuum sector) and those dominated by single excitations of the Fermi vacuum (the 1h1p sector) in heavy atoms (Xe and Hg) and simple molecules of heavy element compounds (I2 and TlF) are reported.

Fock-Space Coupled Cluster Theory: Systematic Study of Partial Fourth Order Triples Schemes for Ionization Potential and Comparison with Bondonic Formalism

In this paper, we have made a systematic study of partial fourth order perturbative schemes due to triples to compute the ionization potential within Fock-space multi-reference coupled-cluster theory. In particular, we have obtained computationally less expensive correlation schemes due to fourth order triples. Prototype examples have been considered to explore the efficacy of the approximate methods mentioned, while the bondonic formalism supporting the bonding phenomenology is also respectively for the first time here advanced.

Equation-of-motion coupled cluster method for the description of the high spin excited states

The equation-of-motion (EOM) coupled cluster (CC) approach in the version applicable for the excitation energy(EE) calculations has been formulated for high spin components. The EE-EOM-CC scheme based on the restricted Hartree-Fock reference and standard amplitude equations as used in the Davidson diagonalization procedure yields the singlet states. The triplet and higher spin components require separate amplitude equations. In the case of quintets, the relevant equations are much simpler and easier to solve. Out of 26 diagrammatic terms contributing to the R1 and R2 singlet equations in the case of quintets, only R2 operator survives with 5 diagrammatic terms present. In addition all terms engaging three body elements of the similarity transformed Hamiltonian disappear. This indicates a substantial simplification of the theory. The implemented method has been applied to the pilot study of the excited states of the C2 molecule and quintet states of C and Si atoms.

Structure, stability, and properties of the trans peroxo nitrate radical: the importance of nondynamic correlation

We report a comparative single-reference and multireference coupled-cluster investigation on the structure, potential energy surface, and IR spectroscopic properties of the trans peroxo nitrate radical, one of the key intermediates in stratospheric NOX chemistry. The previous single-reference ab initio studies predicted an unbound structure for the trans peroxo nitrate radical. However, our Fock space multireference coupled-cluster calculation confirms a bound structure for the trans peroxo nitrate radical, in accordance with the experimental results reported earlier. Further, the analysis of the potential energy surface in FSMRCC method indicates a well-behaved minima, contrary to the shallow minima predicted by the single-reference coupled-cluster method. The harmonic force field analysis, of various possible isomers of peroxo nitrate also reveals that only the trans structure leads to the experimentally observed IR peak at 1840 cm(-1). The present study highlights the critical importance of nondynamic correlation in predicting the structure and properties of high-energy stratospheric NOx radicals.

Reappraisal of nuclear quadrupole moments of atomic halogens via relativistic coupled cluster linear response theory for the ionization process

The coupled cluster based linear response theory (CCLRT) with four-component relativistic spinors is employed to compute the electric field gradients (EFG) of (35)Cl, (79)Br, and (127)I nuclei. The EFGs resulting from these calculations are combined with experimental nuclear quadrupole coupling constants (NQCC) to determine the nuclear quadrupole moments (NQM), Q of the halide nuclei. Our estimated NQMs [(35)Cl = -81.12 mb, (79)Br = 307.98 mb, and (127)I = -688.22 mb] agree well with the new atomic values [(35)Cl = -81.1(1.2), (79)Br = 302(5), and (127)I = -680(10) mb] obtained via Fock space multireference coupled cluster method with the Dirac-Coulomb-Breit Hamiltonian. Although our estimated Q((79)Br) value deviates from the accepted reference value of 313(3) mb, it agrees well with the recently recommended value, Q((79)Br) = 308.7(20) mb. Good agreement with current reference data indicates the accuracy of the proposed value for these halogen nuclei and lends credence to the results obtained via CCLRT approach. The electron affinities yielded by this method with no extra cost are also in good agreement with experimental values, which bolster our belief that the NQMs values for halogen nuclei derived here are reliable.