Dialogue on analytical and ab initio methods in attoscience

Abstract

The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the ‘Quantum Battles in Attoscience’ cecam virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience—covering both analytical and numerical methods—and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in ‘analytical’ techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community.

Analytical model for attosecond time delays and Fano's propensity rules in the continuum

“…The theoretical analysis of these near-threshold processes [11,[13][14][15] can be exclusively carried out through numerical simulations that, despite being extremely useful for an accurate evaluation of the observables, usually provide only partial explanations for the physical origin behind the observed effects. Therefore, the development of a complementary analytical method can be a valuable tool for providing further insights into these phenomena [16].…”

Theoretical study of a derivative of chlorophosphine with aliphatic and aromatic Grignard reagents: SN2@P or the novel SN2@Cl followed by SN2@C?

“…It is known that different methods give different results due to the different level of approximations. [39][40][41][42] This may lead to benchmark studies with respect to such organophosphorus reactions. , of the TSs of the S N 2@P-b, S N 2@P-f, S N 2@Cl and S N 2@C-f pathways Full optimisation with no symmetry constraints was performed using the B3LYP [43][44][45] hybrid functional and the 6-31++G(d,p) basis set in the gas phase.…”

“…It is known that different methods give different results due to the different level of approximations. 39–42 This may lead to benchmark studies with respect to such organophosphorus reactions.…”

Quantum aspects of attoscience

“…This brings a great deal of tension and misconceptions, along with warring schools of thought which favor either type of approach. In this article, Gregory Armstrong, Margarita Khokhlova, Marie Labeye, Andrew Maxwell, Emilio Pisanty and Marco Ruberti try to dispel this tension and find common ground, by critically analyzing the key methods employed in attoscience [ 4 ]. They examine their advantages and shortcomings, their role in scientific discovery and try to find common ground by challenging established beliefs in the attoscience community.…”

“…Over the past three decades, our community has witnessed a great deal of debate over a wide range of topics and unfortunately, although vibrant, this debate has not always been constructive. On a number of issues (see e.g., [ 2 – 4 ]), the attoscience community has tended toward siloed factions holding opposing views. In organizing Quantum Battles in Attoscience we pictured these groups as the scientific equivalent of street gangs, and our proposed solution was to organize a martial-arts-style tournament, with a rigorous code of conduct and where respect would be maintained.…”