Arbitrary-Order Derivatives of Quantum Chemical Methods via Automatic Differentiation.

Herein, we present for the first time a general methodology for obtaining arbitrary-order nuclear coordinate derivatives of electronic energies derived from quantum chemistry methods. By leveraging modern advances in automatic differentiation software, we demonstrate that exact derivatives can be obtained for any method. This innovation completely bypasses the issues associated with the computational stability of applying numerical differentiation methods and dispenses the need to derive challenging formulae for analytic energy derivatives. We describe a freely available and open-source software implementation of our scheme and demonstrate its use in obtaining exact nuclear derivatives of energies from Hartree-Fock theory, second-order Møller-Plesset perturbation theory (MP2), and coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. Our sample computations include up to sextic derivatives and span a variety of test systems with up to 100 basis functions, confirming the viability of this scheme for a wide range of applications. Many of the results obtained have hitherto been unobtainable by exact means due to a lack of higher-order derivative formulae. The details of our implementation and possible further developments are discussed.

Relatives of cyanomethylene: replacement of the divalent carbon by B-, N+, Al-, Si, P+, Ga-, Ge, and As.

The lowest lying singlet and triplet states of HBCN-, HCCN, HNCN+, HAlCN-, HSiCN, HPCN+, HGaCN-, HGeCN, and HAsCN+ were studied using the CCSDT(Q)/CBS//CCSD(T)/aug-cc-pVQZ level of theory. Periodic trends in geometries, singlet-triplet gaps, and barriers to linearity were established and analyzed. The first row increasingly favors the triplet state, with a singlet-triplet gap (ΔEST = Esinglet - Etriplet) of 3.5 kcal mol-1, 11.9 kcal mol-1, and 22.6 kcal mol-1, respectively, for HBCN-, HCCN, and HNCN+. The second row increasing favors the singlet state, with singlet-triplet gaps of -20.4 kcal mol-1 (HAlCN-), -26.6 kcal mol-1 (HSiCN), and -26.8 kcal mol-1 (HPCN+). The third row also favors the singlet state, with singlet-triplet gaps of -26.8 kcal mol-1 (HGaCN-), -33.5 kcal mol-1 (HGeCN), and -33.1 kcal mol-1 (HAsCN+). The HXCN species have larger absolute singlet-triplet energy gaps compared to their parent species XH2 except for the case of X = N+. The effect of the substitution of hydrogen with a cyano group was analyzed with isodesmic bond separation analysis and NBO.