Pseudospectral approach

Gatti F, lung C, Leforestier C and Chapuisat X 1999 Fully coupled 6D calculations of the ammonia vibration-inversion-tunneling states with a split Hamiltonian pseudospectral approach J. Chem. Phys. Ill 7236 3... 

Coupled 6D Calculations of the Ammonia Vibration-Inversion-Tunneling States with a Split Hamiltonian Pseudospectral Approach. 

T. Nakajima, K. Hirao. Pseudospectral approach to relativistic molecular theory. 

A recent development in ab initio quantum theory has been the introduction of (partially) numerical schemes for dealing with the two-electron integrals in a way that reduces the scaling with the size of the system. One of these is the pseudospectral (PS) [12, 13] technique, which is closely related to another procedure known as resolution of the identity (RI) [14-16]. The use of these schemes in conjunction with the LSA has been discussed in detail elsewhere [17]. Here we present just the basic idea behind the PS approach. 

Recently we have proposed more efficient relativistic molecular theory by an application of the pseudospectral (PS) approach [135]. In the PS approach [136,137], we use the mixed basis function between a grid representation in the physical space and spectral representation in the function space. 

The global approach uses an interpolation based on a family of global functions which span all the sampled space with appropriate boundary conditions. This approach which is due to Gauss, is termed collocation (Sec. III.A). In a more elaborate form, based on orthogonal functions it is termed pseudospectral representation (Sec. III.B) (16). Since any local method is global within a small interval we will start by analyzing global approaches. 

Part of these ideas are well discussed in the work of Gottlieb and Orszag (19) and are known as the pseudospectral method. In molecular dynamics this approach is known as DVR (36). 

This is the basic approach in the so-called pseudospectral method. 

In this chapter, we discuss some new developments in TDDFT beyond the linear response regime for accurate and efficient nonperturbative treatment of multiphoton dynamics and very-high-order nonlinear optical processes of atomic and molecular systems in intense and superintense laser fields. In Section 2, we briefly describe the time-dependent optimized effective potential (OEP) method and its simplified version, i.e., the time-dependent Krieger-Li-Iafrate (KLI) approximation, along with self-interaction correction (SIC). In Section 3, we present the TDDFT approaches and the time-dependent generalized pseudospectral (TDGPS) methods for the accurate treatment of multiphoton processes in diatomic and triatomic molecules. In Section 4, we describe the Floquet formulation of TDDFT. This is followed by a conclusion in Section 5. Atomic units will be used throughout this chapter. 

Another exciting new feature of the LMP2 module is the ability to perform multireference perturbation calculations. The approach is based on a GVB formulation of the underlying MC-SCF reference wavefunction, with LMP2 supplying the perturbative corrections. Pseudospectral methods are employed to enhance the performance of both components, thus enabling highly correlated calculations at a fraction of the cost of conventional implementations. 

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