A radical molecule contains one or more electrons that are unpaired. A radicaloid may be defined as a molecule in which there are that are partially unpaired. As a result, the electronic structure of the radicaloid can be quite complicated for a variety of reasons. For a singlet biradicaloid, the singlet and triplet wavefunction can be quite close energetically which can lead to problems when trying to describe the system with a single determinant. The simplest solution to this problem is to allow the wavefunction to break spin-symmetry in order to get a lower energy. Unfortunately this action can lead to wavefunctions that are no longer eigenfunctions of the operator. In the second chapter we investigate a distannyne which has a biradicaloid resonance structure. By examining the orbital Hessian, it is discovered that the spin-symmetric solution is a saddle-point in wavefunction space and is structurally different than the spin-polarized solution. We then increase the complexity of the model system and see that the spin-symmetric solution is only a minimum for the exact experimental system and not for a simplified model system in which bulky organic substituents are replaced by simpler phenyl groups. Therefore, the breaking of spin-symmetry is absolutely critical in the small model systems and the full substituents play a non-trivial role. However, the breaking of the spin-symmetry can have consequences for physical quantities when correlated methods are used. At the point of spin polarization or unrestriction the orbital Hessian will have one eigenvalue which is zero. Since the relaxed density matrix in correlated methods like Second-Order M\o ller-Plesset theory (MP2) depend on the inverse of the Hessian, at the unrestriction point this quantity will be undefined. Some unphysical artifacts are identified as a direct consequence of this fact. First, discontinuities in first order molecular properties such as the dipole moment are seen at the geometries associated with unrestriction. Second, the relaxed density matrix itself fails to be N-representable, with natural orbital occupation numbers less than zero and greater than one. Therefore, it is desirable to use a method that is not dependent on the inverse of the Hessian like orbital optimized MP2 (O2).Another system which requires the use of orbital optimization is a neutral soliton on a polyacetylene chain. In this system, the Hartree-Fock reference suffers from severe spin-polarization making the wavefunction physically unreasonable unless a very sophisticated treatment of electron correlation is used to correct this problem. Originally, it was found that computationally expensive methods like CCSD(T) and CASSCF could adequately describe small model chain but not the full system. The O2 method is found to be an dramatic improvement over traditional MP2 which can be feasibly applied to polyenyl chains long enough to characterize the soliton. It is also discovered that density functionals are generally inadequate in describing the half-width of the soliton.Finally, the last chapter takes a slightly different perspective and focuses on the addition of correlation energy to a successful energy decomposition analysis based on absolutely localized molecular orbitals. It is discovered that the resulting new method can adequately describe systems with dispersive intermolecular interactions and large amounts of charge transfer. This scheme is then applied to the water dimer systems and it is found that all of the intermolecular interactions similar in size with the electrostatic interaction being the largest and the dispersive interaction being the smallest. This method is also contrasted with other EDA schemes
