Radicals are highly reactive chemical species with one or more unpaired electron(s). Depending on the number of unpaired electrons, they are classified into monoradicals, diradicals, triradicals, etc. Due to the potential role as molecular magnets, polyradicals have caught attention of chemists. The near-degeneracies in the electronic states results in interesting bonding patterns and chemical reactivity of the radicals. We are interested to study the bonding-patterns, thermochemistry and analytical physical properties of radicals using various coupled-cluster methods

Equation-of-motion (EOM) coupled-cluster (CC) methods have been extensively used by computational chemists for studying the non-dynamical electron correlation effects because of the compactness and simplicity of the methods arising from single reference (SR) framework. EOM-CC with spin-flip (SF) method projects various singly and doubly excited states as singly excited target states with respect to a suitable high-spin reference state and yields size-intensive difference energies. The EOM-CC with spin-conserving excited states (EE) also are size-intensive except the charge-transfer states.Similarly, EOM-CC also offers anasatz for ionized states (IP), electron-attached states (EA) and so on.

EOM-SF/EE-CC with single and double substitutions (SD) compute the excitation energies for singly excited states with an accuracy of 0.1-0.01 eV. This error bar becomes prominent for some close-lying states and more accuracy is demanded in order to correctly compute the spectroscopic parameters. While the most straightforward approach of complete inclusion of three-body and higher substitutions is conceptually simple and accurate, it turns out to be computationally challenging, thereby hindering the applicability of the method to only small molecules. The intermediate corrections like EOM-CC(2,3) also cannot avoid the storage of six-index tensors and has limited applicability.

We proposed a non-iterative perturbative correction to EOM-CCSD anasatz which avoids the storage of six-index tensors. In our method, the EOM-CCSD Hamiltonian matrix plus diagonal of the triples block computed using CCSD vectors is taken as the zeroth-order picture of the system. The off-diagonal part of the triples block (couplings within triples and of triples with singles and doubles) is incorporated via Rayleigh Schrodinger perturbative scheme to obtain a second order correction to the EOM-CCSD energy. This correction serves as approximation to EOM-CCSDT or EOM-CC(2,3) and being compact and cost-effective, can be applied to study electronic structure of moderately big molecules. We coded and used the correction denoted as "(dT)" or "(fT)" (depending on the choice of the terms in the expression for the diagonal for EOM-SF-CCSD and EOM-IP-CCSD methods.  Our work has been incorporated in Q-CHEM version 3.2.

Molecular properties are obtained by studying the response of the system to an external perturbation. Linear response approach is one of the most approach-of-choice because of the simplicity and accuracy of the approach. The properties calculated in this way are termed as response properties. Response properties are characteristics of the various interactions between the moving charges and strongly depend on the molecular state. While the response properties can be easily calculated for ground and some non-degenerate states of molecules, the situations like ionization, electron-attachment, electronic excitations are challenging because of the significant non-dynamical electron correlation resulting from the near-degeracy of the electronic states. Fock-space (FS) multi-reference (MR) coupled-cluster (CC) method is one of the cost-effective methods that efficiently studies the non-dynamical as well as dynamical electron-correlation effects without compromising on size-consistency, size-extensivity and accuracy. Clearly, the response properties of these challenging states can be obtained by studying the effects of external perturbation to the FSMRCC anasatz. We have developed codes for the constrained-variational response approach to FSMRCC and used them to compute analytical dipole moments and analytical frequency-independent dipole polarizabilities of monoradicals and molecules in high-spin states.