The self-consistent electron pairs method for multiconfiguration reference state functions

Abstract

An efficient direct CI method which includes all singly and doubly substituted configurations with respect to an arbitrary multiconfiguration (MCSCF) reference function is described. The configurations are generated by subsequently applying spin-coupled two-particle annihilation and creation operators to the complete MCSCF function. This considerably reduces the size of the n-electron basis and the computational effort as compared to previous multireference CI treatments, in which the configurations are defined with respect to the individual reference configurations. The formalism of the method is very similar to the closed-shell ’’self-consistent electron pairs’’ (SCEP) method of Meyer. The vector Hc is obtained in terms of simple matrix operations involving coefficient and integral matrices. A full transformation of the two-electron integrals is not required. Test calculations with large basis sets have been performed for the 3B1 and 1A1 states of CH2 (ΔE = 9.5 kcal/mol) and for the CH2(3B1) +H2→CH3+H reaction barrier (ΔE = 10.7 kcal/mol). As a preliminary test for the accuracy of the results obtained with contracted wave functions of the above type the potential energy and dipole moment functions of the OH X 2Π and A 2Σ+ states have been calculated. For the 2Π state re and ωe deviate by less than 10−3 Å and 1 cm−1, respectively, from the experimental data. For the 2Σ+ state the agreement is somewhat less good, which is probably due to basis set defects. Around the equilibrium distance the calculated dipole moment functions are in very close agreement with those previously obtained from PNO– CEPA functions.

Spin-adapted density matrix renormalization group algorithms for quantum chemistry

“…30,31,[38][39][40] Algorithms to efficiently evaluate one-and two-body density matrices from DMRG wavefunctions have been described earlier 41,42 and we refer the reader to those references for details. The efficient evaluation of the two-body reduced density matrix is most convenient in the "one-dot" formulation (see Sec.…”

Interactions and dynamics in Li+Li2 ultracold collisions

“…3 shows the triplet states of Li 2 calculated using ͓2,8͔-CASSCF, followed by an internally contracted multireference configuration interaction 34,[37][38][39] ͑MRCI͒ including single and double excitations from the CASSCF wave function. Figure 4 shows a correlation diagram that connects the D ϱh , D 3h , and atom-diatom ͑C 2v ͒ limits for states of quartet Li 3 that correlate with the S + S + P atomic limit for a fixed bond length of 6 Å.…”

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

“…An efficient approach for this is to treat excitations out of a qualitatively correct, strongly correlated reference function. Methods of this class are hierarchies based on truncated multireference configuration interaction (MRCI) 10,35,36 , various flavors of perturbation theory 6,37-39 and coupled cluster theory. 40,41 However, the established methods of these classes are based on CI treatments of the static correlation, which either makes them cumbersome to apply (RAS, GAS) [42][43][44] , or limits them to small active spaces (CAS).…”

“…We here focus on DMRG, 20,21 a variational method which minimizes the energy of a wavefunction parametrized as a matrix product state (MPS). 22,23 DMRG can handle active spaces of around [30][31][32][33][34][35][36][37][38][39][40] orbitals, and in some cases even up to 100 [24][25][26][27][28][29][30][31][32][33][34] . However, by themselves the mentioned methods are not efficient for obtaining quantitative accuracy and for this dynamic correlation must also be calculated.…”