Large vibrational variational calculations using 'multimode' and an iterative diagonalization technique

We have favoured the variational (secular equation) method for the determination of the (ro-) vibrational energy levels of polyatomic molecules. We use predominantly the Watson Hamiltonian in normal coordinates and an associated given potential in the variational code 'Multimode'. The dominant cost is the construction and diagonalization of matrices of ever-increasing size. Here we address this problem, using pertubation theory to select dominant expansion terms within the Davidson-Liu iterative diagonalization method. Our chosen example is the twelve-mode molecule methanol, for which we have an ab initio representation of the potential which includes the internal rotational motion of the OH group relative to CH3. Our new algorithm allows us to obtain converged energy levels for matrices of dimensions in excess of 100 000.

Rotational aesthetics: Michael Bay and contemporary cinema’s machine movement

Digital imaging technologies enable a mastery of the visual that in recent mainstream cinema frequently manifests as certain kinds of spatial reach, orientation and motion. In such a context Michael Bay’s Transformers franchise can be framed as a digital re-tooling of a familiar fantasy of vehicular propulsion, US car culture writ large in digitally crafted spectacles of diegetic speed, the vehicular chase film ‘2.0’. Movement is central to these films, calling up Scott Bukatman’s observation that in spectacular visual media ‘movement has become more than a tool of bodily knowledge; it has become an end in itself’ (2003: 125). Not all movements and not all instances of vehicular propulsion are the same however. How might we evaluate what is at stake in a film’s assertion of movement as an end in itself, and the form that assertion takes, its articulations of diegetic velocity, corporeality, and spatial penetration? Deploying an attentiveness towards the specificity of aesthetic detail and affective impact in Bay’s delineation of movement, this essay suggests that the franchise poses questions about the relationship of human movement to machine movement that exceed their narrative basis. Identifying a persistent rotational trope in the franchise that in its audio-visual articulation combines oddly anachronistic elements (evoking the mechanical rather than the digital), the article argues that the films prioritise certain fantasies of transformation and spatial penetration, and certain modes of corporeality, as one response to contemporary debates about digital technologisation, sustainable energy, and cinematic spectacle. In this way the franchise also represents a particular moment in a more widely discernible preoccupation in contemporary cinema with what we might call a ‘rotational aesthetics’ of action, a machine movement made possible by the digital, but which invokes earlier histories and fantasies of animation, propulsion, mechanization and mechanization to particular ends.