UC Berkeley

Correlation methods within electronic structure theory focus on recovering the exact electron-electron 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 short- and 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 inter- and 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 inter- and 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 basis MP2. A variety of tests including the S22 set, conformer energies of peptides, alkanes, sugars, sulfate-water clusters, and the coronene dimer establish the transferability of the MP2(terfc, aTZ) model to other inter and intra-molecular interactions. Direct comparisons against attenuation in the smaller aug-cc-pVDZ basis shows that MP2(terfc, aTZ) often significantly outperforms MP2(terfc, aDZ), although at higher computational cost. MP2(terfc, aDZ) and MP2(terfc, aTZ) often outperform MP2 at the complete basis set limit. Comparison of the two attenuated MP2 models against each other and against attenuation using non-augmented basis sets gives insight into the error cancellation responsible for their remarkable success.

Third, I present an improved algorithm for single-node multi-threaded computation of the correlation energy using resolution of the identity second-order Møller-Plesset perturbation theory (RI-MP2). This algorithm is based on shared memory parallelization of the rate-limiting steps and an overall reduction in the number of disk reads. The requisite fifth-order computation in RI-MP2 calculations is efficiently parallelized within this algorithm, with improvements in overall parallel efficiency as the system size increases. Fourth-order steps are also parallelized. As an application, I present energies and timings for several large, noncovalently interacting systems with this algorithm, and demonstrate that the RI-MP2 cost is still typically less than 40% of the underlying self consistent field (SCF) calculation. The attenuated RI-MP2 energy is also implemented with this algorithm, and some new large-scale tests of this method are reported. The attenuated RI-MP2(terfc, aug-cc-pVDZ) method yields excellent agreement with benchmark values for the L7 database (R. Sedlak et al., J. Chem. Theory Comput. 2013, 9, 3364) and 10 tetrapeptide conformers (L. Goerigk et al., Phys. Chem. Chem. Phys. 2013, 15, 7028), with at least a 90% reduction in the root-mean-squared (RMS) error versus RI-MP2/aug-cc-pVDZ.

Fourth, semi-empirical spin-component scaled (SCS) attenuated MP2 is developed for treating both bonded and nonbonded interactions. SCS-MP2 improves the treatment of thermochemistry and noncovalent interactions relative to MP2, although the optimal scaling coefficients are quite different for thermochemistry versus noncovalent interactions. This work reconciles these two different scaling regimes for SCS-MP2 by using two different length scales for electronic attenuation of the two spin components. The attenuation parameters and scaling coefficients are optimized in the aug-cc-pVTZ (aTZ) basis using the S66 database of intermolecular interactions and the W4- 11 database of thermochemistry. Transferability tests are performed for atomization energies and barrier heights, as well as on further test sets for inter- and intramolecular interactions. SCS dual- attenuated MP2 in the aTZ basis, SCS-MP2(2terfc, aTZ), performs similarly to SCS-MP2/aTZ for thermochemistry while frequently outperforming MP2 at the complete basis set limit (CBS) for nonbonded interactions.

Finally, I examine the performance of attenuated MP2 for noncovalent interactions using basis sets that range as high as augmented triple (T) and quadruple (Q) zeta with TQ extrapolation towards the complete basis set (CBS) limit. By comparing training and testing performance as a function of basis set size, the effectiveness of attenuation as a function of basis set can be assessed. While attenuated MP2 with TQ extrapolation improves systematically over MP2, there are at most small improvements over attenuated MP2 in the aug-cc-pVTZ basis. Augmented functions are crucial for the success of attenuated MP2.