Demanding Computational Strategies

The modes of thinking about structures and reactions and intermediates facilitated or even demanded by these conceptual innovations meshed productively with new tools of a different sort to drive the progress of recent decades. Advances in electronics and computers, all sorts of spectroscopy, laser optics and physics, chromatography, mass spectrometry, quantum theory and computational strategies, molecular beam experiments, and so on, radically expanded the limits of experimental and theoretical investigations. 

The rapid advent of computational power and re-chargeable lithium batteries was in many ways simultaneous in the early 1990s - but not coupled to each other to a large extent at the time of the breakthroughs. However, as the new computers and computational methods were efhcient, these fast became used in the field to model well-known battery materials and phenomena, often with the aim to explain experimental data. Later there were also new battery materials or demands emerging, where computations were foreseen to possibly have a predictive power. As another way of thinking, the models needed to correctly look at complex battery phenomena spurred the development of computational strategies and methods. 

The systematic computational strategy outlined in this section of the review is necessary albeit demanding. The approach provides an accurate description of the entire spectrum of noncovalent interactions between fragments in a cluster. One can be confident in the calculated results regardless of cluster composition [i.e., whether examing the (HiOls, (CgH6)2, or a mixture of the two]. Less obviously but more importantly, one can also be confident in the calculated results across the entire (intermolecular) potential energy... 

The boundary conditions too were known. It would not be as easy as handling an infinite periodic solid, but a number of us set to work. The special demand of chemistry was to quantify very small molecular changes. Successes came slowly, but with the development of computers and a lot of careful, clever work, by the 90s the quantitative problem was essentially solved. The emergent hero of the chemical community was John Pople, whose systematic strategy and timely method developments were decisive. The methods of what is termed ab initio quantum chemistry became available and used everywhere. 

Most numerical methods for calculating molecular hyperpolarizability use sum over states expressions in either a time-dependent (explicitly including field dependent dispersion terms) or time-independent perturbation theory framework [13,14]. Sum over states methods require an ability to determine the excited states of the system reliably. This can become computationally demanding, especially for high order hyperpolarizabilities [15]. An alternative strategy adds a finite electric field term to the hamiltonian and computes the hyperpolarizability from the derivatives of the field dependent molecular dipole moment. Finite-field calculations use the ground state wave function only and include the influence of the field in a self-consistent manner [16]. 

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