Developments in coupled-cluster theory gradients and potential energy surfaces

Despite the successes of coupled-cluster theory (CC) to predict the properties of small- and medium-sized molecules of chemical interest, there are limitations to the conventional approach. The computational cost of the "gold standard" CCSD(T) method scales as O(N7) in the number of electrons, limiting the size of systems that can be calculated. Also, CCSD(T) performs relatively poorly away from equilibrium. This study proposes and evaluates partial solutions to those and related problems of coupled-cluster theory.;The frozen natural orbital (FNO) coupled-cluster method increases the speed of coupled-cluster calculations by an order of magnitude with no consequential error along a potential energy surface. This method allows the virtual space of a correlated calculation to be reduced by about half, significantly reducing the time spent performing the coupled-cluster calculation. The derivation of both the energy and gradient for FNO-CC and applications to energetic material are presented.;The failure of CCSD(T) away from equilibrium is shown to arise from two separate effects. For spin-restricted references, near degeneracy in the orbital space leads to problems with the (T) perturbative correction. For spin-unrestricted references, it is the slow convergence of perturbation theory due to spin-contamination that is the problem. The first of these problems is addressed by using ΛCCSD(T), a method of the same computational scaling as CCSD(T), that, by using information from CC gradient calculations, improves the description of stretched bonds. To efficiently derive the gradient expression for ΛCCSD(T) a more general form of the coupled-cluster energy is functional is introduced, allowing the method to be formulated in a stationary manner.;The spin-symmetry breaking problem is addressed by using Brueckner orbitals to make the spin-restricted solution more stable across a potential energy surface. This choice then naturally leads to Brueckner ΛCCSD(T), which is shown to improve the behavior of bond-breaking beyond ΛCCSD(T) itself.;To more fundamentally address the problem of potential energy surfaces, hermitian coupled-cluster theories deriving from expectation-value CC (XCC) are explored. Linearized CC is shown to be an economical method that, using a simple numerical regularization procedure, generates well-behaved potential energy surface. The capabilities of various other modifications of XCC and its truncations are explored. These purely theoretical investigations suggest that XCC-based methods have the potential to improve the capabilites of CC.