RI-MP2 method

Bernholdt, D. E. Harrison, R. J. Large-scale correlated electronic structure calculations the RI-MP2 method on parallel computers, Chem. Phys. Lett. 1996, 250, 477-484. 

Recently, Hobza has reviewed various theoretical methods used to predict the stabilization energies of extended H-bonding systems [150, 182], The capability of resolution of identity (RI) MP2 method has been assessed with Dunning s correlation consistent basis sets. The need for BSSE corrections for geometries, vibrational frequencies, and other properties of extended H-bonded systems has been stressed. The failure of DFT-based methods to describe the dispersion energy component in the prediction of H-bonding of extended aromatic systems has also been illustrated [182]. 

Only the computationally cheapest post-HF method can be currently applied on zeolites. Computationally the fastest and most popular post-HF method is perturbation theory considering up to the second order terms (MP2 method, using a Moller-Plesset formulation for the correlation energy).[8] This method is not variational and typically it overestimates the effect of the electron correlation. When the resolution of identity (RI) approximation ] is used the RI-MP2 method can be used for calculations on systems consisting of more than hundred atoms. 

A different approach to dynamical correlation in large systems is to approximate the four-center two-electron integrals in, for example, Eq. (53) by sums of products of three-center integrals, as done in the resolution-of-identity MP2 (RI-MP2) method [64]. As the number of three-center integrals is much smaller than the number of four-center integrals, this approach reduces the computational cost of MP2 calculations dramatically. To ensure high accuracy in the calculations, special auxiliary basis sets have been developed for the RI expansion. Although the RI expansion... 

Correlated Electronic Structure Calculations The RI-MP2 Method on Parallel Computers. 

The second aspect listed is of great advantage in MP2 treatments leading to spectacular reductions in CPU and disc space requirements of the RI-MP2 method as compared with conventional MP2. 

At the heart of the RI-MP2 method is an expansion of the shell pairs l/rv) in an auxiliary basis of atom-centered Gaussians, fC). This allows the four-index electron repulsion integrals required in MP2 theory to be expressed in terms of three-index integrals ... 

The HF method tends to overestimate the barriers, making unstable molecules seem stabler than they really are. Geometries are discussed further in Section 5.5.1. Approximate versions of the MP2 method that speed up the process with little loss of accuracy are available in some program suites LMP2, localized MP2, and RI-MP2, resolution of identity MP2. LMP2 starts with a Slater determinant which has been altered so that its MOs are localized, corresponding to our ideas of bonds and lone pairs (Section 5.2.3.1), and permits only excitations into spatially nearby virtual orbitals [93]. RI-MP2 approximates four-center integrals (Section 5.3.2) by three-center ones [94]. 

Figure 12-3. IR-UV double resonance spectrum of GC (structure C) in the mid-IR frequency range (recorded at the FELIX free electron laser facility), compared with three types of ab intio calculations. Harmonic frequencies were obtained at the RI-MP2/cc-pVDZ, RI-MP2/TZVPP, and semiempirical PM3 levels of electronic structure theory. Anharmonic frequencies were obtained by the CC-VSCF method with improved PM3 potential surfaces [30]...

Second-order Moller-Plesset perturbation theory (MP2) is the computationally least expensive and most popular ab initio electron correlation method [4,15]. Except for transition metal compounds, MP2 equilibrium geometries are of comparable accuracy to DFT. However, MP2 captures long-range correlation effects (like dispersion) which are lacking in present-day density functionals. The computational cost of MP2 calculations is dominated by the integral transformation from the atomic orbital (AO) to the molecular orbital (MO) basis which scales as 0(N5) with the system size. This four-index transformation can be avoided by introduction of the RI integral approximation which requires just the transformation of three-index quantities and reduces the prefactor without significant loss in accuracy [36,37]. This makes RI-MP2 the most efficient alternative for small- to medium-sized molecular systems for which DFT fails. 

As auxiliary RI correlation consistent basis sets have been optimized, an RI-ccCA implementation was created by Prascher and Wilson [154], replacing all MP2 steps with their equivalent RI-MP2 computations, and the CCSD(T)-additive correction with the local RI-CCSD(T) method developed by Schiitz and Werner [159-161]. Correlation consistent auxiliary basis sets developed by Weigend [162] were utilized for the various ccCA steps. Benchmark computations on 102 closed... 

The paper by Bemholdt also examined the scalability of MP2 calculations but in this case the emphasis was on the exploitation of parallel computing methods in MP2 calculations using the so-called "RI-MP2 in which approximations based on the resolution of the identity are used in performing the sum over states. 

From our Rl-PBE calculations, we found that various reactant complexes between alkanes and ZSM-5 have very similar value for a and the value of 6.56 gave the best fit. A similar observation could also be noticed for RI-MP2 calculations. In addition, there has been a report [23] that the a value depends mainly on method and basis set and it does not vary much for the molecular system with the same set of atoms. Thus, values of a from RI-PBE and RI-MP2 calculations were later used to determine CBS limit at 38T model through Eq. (5) proposed by Truhlar et al. [23]. 

Electronic energies for a given molecular structure can be computed on the SCF, DFT, and MP2 level for closed shell states, and for open shell states within the UHF description. Open shell ROHF treatments are supported for the SCF method. All common DFT functionals are implemented, including the hybrid functionals which include exact exchange, e.g., modified BLYP (B3LYP). Treatments within the non-hybrid functionals can be efficiently earned out in the RI mode. Version 4.1 will support the efficient RI-MP2 technique. 

In particular, electron correlation effects are crucial to describe the vdW interaction. To account for the electron correlation effects, density functional theory (DFT) is widely used. As the former interaction is mainly caused by electrostatic interaction between the base pairs, it is sufficient to describe it with the hybrid DFT methods. On the other hand, it is rather difficult to describe the latter interaction by means of the standard hybrid DFT because of the lack of the weak dispersion force. The latter interaction is so weak that the post Hartree-Fock (HF) theories such as the second order of Mpller-Presset perturbation theory (MP2) and coupled-cluster method (CC) are at least required to describe it qualitatively. In 2004, Hobza et al. estimated accurate interaction energies between stacked bases by using MP2 based on the resolution of identity method (RI-MP2), with complete basis set (CBS) corrections [1,2]. 

---