The multi-configurational time-dependent Hartree approach

1 The multi-configurational time-dependent Hartree approach 

In the multi-configurational time-dependent Hartree (MCTDH) approach [24, 25], the wavefunction V (xi,. .,Xf,t) is represented as 

The (t) are time-dependent expansion coefficients. The time-dependent 

DVR or FFT-schemes can be used to represent these single-particle functions  

The MCTDH-representation of the wavefunction should be compared to the representation of the wavefunction employed in a standard wavepacket scheme  

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Meyer, H.-D., Manthe, U., and Cederbaum, L.S. (1990). The multi-configurational time-dependent Hartree approach, Chem. Phys. Lett. 165, 73-78. 

The Hamiltonian in Eq. (4.1) has an almost product-like form since the majority of coordinates are treated as harmonic oscillators. This makes it rather suitable for quantum dynamics simulations, either in the time-dependent Hartree approximation [31] or using the more general multi-configuration time-dependent Hartree approach [36, 37]. 

Hammer T, Manthe U (2012) Iterative diagonalization in the state-averaged multi-configurational time-dependent Hartree approach excited state tunneling splitting in malonaldehyde. J Chem Phys 136 054105... 

UV spectra usually involve electronic state transitions, so that simple Hartree-Fock and DFT calculations often are not sufficient PCM has been recently extended also to multi-configurational (MC-SCF) calculations [113] and to time-dependent approaches, allowing for the description of excited states and then the prediction of the so-called solvatochromic effects on these spectra. Nuclear magnetic resonance (NMR) and electron spin resonance (EPR) spectra are even more influenced by solute-solvent interactions moreover, the interpretation of experimental data is often very difficult without the support of reliable ab initio calculation, especially for EPR which is usually applied to unstable radical species. 

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