Range Correlation Models in Electronic Structure Theory

Short-Range Correlation Models in Electronic Structure Theory by Matthew Bryant Goldey Doctor of Philosophy in Chemistry University of California, Berkeley Professor Martin Head-Gordon, Chair Correlation methods within electronic structure theory focus on recovering the exact electronelectron interaction from the mean-field reference. For most chemical systems, including dynamic correlation, the correlation of the movement of electrons proves to be sufficient, yet exact methods for capturing dynamic correlation inherently scale polynomially with system size despite the locality of the electron cusp. This work explores a new family of methods for enhancing the locality of dynamic correlation methodologies with an aim toward improving accuracy and scalability. The introduction of range-separation into ab initio wavefunction methods produces short-range correlation methodologies, which can be supplemented with much faster approximate methods for long-range interactions. First, I examine attenuation of second-order Møller-Plesset perturbation theory (MP2) in the aug-cc-pVDZ basis. MP2 treats electron correlation at low computational cost, but suffers from basis set superposition error (BSSE) and fundamental inaccuracies in long-range contributions. The cost differential between complete basis set (CBS) and small basis MP2 restricts system sizes where BSSE can be removed. Range-separation of MP2 could yield more tractable and/or accurate forms for shortand long-range correlation. Retaining only short-range contributions proves to be effective for MP2 in the small aug-cc-pVDZ (aDZ) basis. Using one range-separation parameter within either the complementary error function (erfc) or a sum of two error functions (terfc), superior behavior is obtained versus both MP2/aDZ and MP2/CBS for interand intra-molecular test sets. Attenuation of the long-range helps to cancel both BSSE and intrinsic MP2 errors. Direct scaling of the MP2 correlation energy (SMP2) proves useful as well. The resulting SMP2/aDZ, MP2(erfc, aDZ), and MP2(terfc, aDZ) methods perform far better than MP2/aDZ across systems with hydrogen-bonding, dispersion, and mixed interactions at a fraction of MP2/CBS computational cost. Second, attenuated MP2 is developed within the larger aug-cc-pVTZ (aTZ) basis set for interand intramolecular non-bonded interactions. A single attenuation parameter is optimized on the S66 database of 66 intermolecular interactions, leading to a very large RMS error reduction by a factor of greater than 5 relative to standard MP2/aTZ. Attenuation introduces an error of opposite sign to basis set superposition error (BSSE) and overestimation of dispersion interactions in finite