An exotic molecular inventory exists in space. While some species have well-known terrestrial analogs, others are very reactive and can hardly survive in the laboratory timely to allow for their characterization. With an eye toward these latter, we highlight in this contribution the role of quantum chemistry in providing astrochemically relevant data where experiment struggles. Special attention is given to the concept of molecular potential energy surfaces (PESs), a key aspect in theoretical chemical physics, and the possible dynamical attributes taken therefrom. As case studies, we outline our current efforts in obtaining global PESs of carbon clusters. It is thus hoped that, with such an active synergy between theoretical chemistry and state-of-the-art experimental/observational techniques (the pillars to the modern laboratory astrophysics), scientists may gather the required knowledge to explain the origins, abundances and the driving force toward molecular complexity in the Universe.

The Coupled Cluster (CC) method is a widely used and highly successful high precisionmethod for the solution of the stationary electronic Schrödingerequation, with its practical convergence properties being similar to that of acorresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method beenanalyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in[Schneider, 2009]. Recently, we globalized the CC formulation to the full continuousspace, giving a root equation for an infinite dimensional, nonlinear Coupled Clusteroperator that is equivalent the full electronic Schrödinger equation [Rohwedder, 2011]. Inthis paper, we combine both approaches to prove existence and uniqueness results,quasi-optimality estimates and energy estimates for the CC method with respect to thesolution of the full, original Schrödinger equation. The main property used is a localstrong monotonicity result for the Coupled Cluster function, and we give twocharacterizations for situations in which this property holds.

Nowadays, the Coupled Cluster (CC) method is the probably most widely used high precisionmethod for the solution of the main equation of electronic structure calculation, thestationary electronic Schrödinger equation. Traditionally, theequations of CC are formulated as a nonlinear approximation of a Galerkin solution of theelectronic Schrödinger equation, i.e. within a given discrete subspace.Unfortunately, this concept prohibits the direct application of concepts of nonlinearnumerical analysis to obtain e.g. existence and uniqueness results orestimates on the convergence of discrete solutions to the full solution. Here, thisshortcoming is approached by showing that based on the choice of anN-dimensional reference subspace R of H1(ℝ3 ×{± 1/2}), the original, continuous electronic Schrödingerequation can be reformulated equivalently as a root equation for an infinite-dimensionalnonlinear Coupled Cluster operator. The canonical projected CC equations may then beunderstood as discretizations of this operator. As the main step, continuity properties ofthe cluster operator S and its adjoint S† asmappings on the antisymmetric energy space H1 are established.

This study was motivated by the fact that some amino acids are currently identified in carbonaceous chondrites but none are yet observed in the interstellar medium. The question of the relative stability of these prebiotic compounds with respect to the other possible species of the same chemical formula is addressed by means of quantum chemical simulations based on density functional theory (DFT). A preliminary investigation of molecules with the formula C2H5O2N shows that glycine (H2NCH2COOH) is not the most stable compound that can be formed: it is ~10 kcal mol−1 higher in energy than CH3NHCOOH, which becomes the most likely candidate for a search in space. The same argument of relative stability used to explained why formamide H2N-HC=O was identified in the interstellar medium (rather than any of its isomers) provides here a rationalization of the permanent debate about the detection of glycine. A second investigation of protonated derivatives of the same series that may result from ion molecule chemistry shows that under its nitrogen protonated form (H3N+CH2COOH) glycine does become the most stable compound. This suggests that, if glycine presently detected in chondrites has an interstellar origin, it must have been synthetized as its protonated form by ion–molecule processes. A similar study was carried out on the corresponding glycine N-carboxyanhydride. The calculated rotational constants (GHz) of glycine A=10.3603; B=3.8590; C=2.9037 (Exp: 10.3418; 3.8762; 2.9123, respectively) served as the benchmark to derive the correcting factors necessary to estimate the rotational constants of the possible candidates within a few tenths of a percent. The dipole moments were determined and the values in the range 4–6 Debye obtained for the protonated species should be large enough to initiate laboratory experiments and/or observations. Theoretical infrared spectra are also provided to assist in the identification of these exotic species.

This paper looks at the possibility that the peptide bond may be more common than originally thought, leading to molecules of prebiotic interest containing heavier atoms of the second row of the periodic table. Ab initio Möller–Plesset (MP2) coupled-cluster molecular orbital methods and density functional theory have been used. A first investigation of the six-atom system [C,3H,O,N] showed that formamide, NH2[bond]CH[double bond]O, is the most stable system that can be formed. Systematic studies on this same system in which C, O and N were respectively replaced by Si, S and P were then carried out. It has been found that the peptide-like linkage is the most stable for [C,3H,S,N] and [Si,3H,O,N] where NH2[bond]CH[double bond]S and NH2[bond]SiH[double bond]O are about 10–14 kcal mol−1 more favourable than the corresponding enol tautomers and well below other isomers on the energy scale. For [C,3H,O,P], the most stable species is CH3[bond]P[double bond]O, which is found 18 kcal mol−1 below the PH2[bond]CH[double bond]O peptide analogue. By correcting the known inadequacies in the calculations with the average theoretical to experimental ratio from the benchmark molecules of the system, it is possible to obtain a best estimate of rotational constants and infrared frequencies that should be precise enough to initiate laboratory experiments and/or observations. The corrected values of B=6.0342 GHz and C=5.4921 GHz for NH2[bond]CH[double bond]S; B=9.2292 GHz and C=6.1164 GHz for NH2[bond]SiH[double bond]O; B=8.0275 GHz and C=6.4779 GHz for CH3[bond]P[double bond]O should be accurate to within a few tenths of a per cent. Theoretical infrared spectra are also provided to assist in identification of these exotic species.