Unraveling Excited States of Doped Helium Clusters † Tatjana S ˇ krbic ´ , £ Saverio Moroni,* and Stefano Baroni ‡ SISSAsScuola Internazionale Superiore di Studi AVanzati, and CNR-INFM DEMOCRITOS National Simulation Center, Via Beirut 2-4, 34014 Trieste, Italy ReceiVed: August 2, 2007; In Final Form: October 17, 2007 We discuss the use of generalized, symmetry-adapted, imaginary-time correlation functions to study the rotational spectrum of doped helium clusters within the frame of the reptation quantum Monte Carlo method. Analysis of these correlation functions allows one to enhance the computational efficiency in the calculation of weak spectral features, as well as to get a qualitative insight into the nature of the different lines. The usefulness of this approach is demonstrated by a study of the He-CO binary complex, used as a benchmark case, as well as by preliminary results for the satellite band recently observed in the IR spectrum of the CO 2 molecule solvated in He nanodroplets. The spectroscopic interrogation of molecules individually embedded in superfluid He nanodroplets, pioneered by Scoles in the early 90s, 1 has spawned an ever increasing number of experimental and theoretical works aimed at elucidating the interplay between the molecular rotational and vibrational features of the spectrum and the structure of the He matrix. 2-5 One of the most spectacular features that emerges from the resulting rich phenomenology is the free-rotor character of the rotational spectrum, with a molecular inertia that is increased with respect to its gas-phase value. This behavior is intimately related to the most fundamental physical property of the quantum solvent, namely, its superfluid character, which persists down to extremely small system sizes. 6,7 Superfluidity (which can be traced back to the scarcity of low-energy excitations in this confined interacting boson system), together with the mildness of the He-molecule interaction, makes He droplets, in a sense, the ultimate spectroscopic matrix. 8 While considerable progress has been made in the under- standing of the fundamental properties of these systems (such as, e.g., their structure and its relation to superfluidity, the turnaround between a classical to a superfluid behavior of the host, as a function of the system size, etc.), many subtle features of the observed spectra still remain to be understood. For instance, the residual interaction between the effective rotor (constituted by the molecule together with part of the He density dragged around by it) and the rest of the host gives rise to such phenomena as line broadening and splitting and satellite bands (faint spectral features that would be absent in the spectrum of a rigid rotor), which still escape a proper theoretical understand- ing. Examples of these effects include the splitting of the R(0) lines in the spectra of small CO@He N clusters, 11 as well as the satellite band that is observed to accompany the strong and sharp R(0) rovibrational line in the infrared spectra of He-solvated CO 2 . 12 Much of this progress is due to recent advances in the quantum simulation technology that is currently capable of providing microscopic information not easily accessible (or not accessible at all) to experiment. Thanks to these advances, the scope of quantum Monte Carlo simulations of interacting bosons is being extended from the structure of the ground state to the dynamical regime, at least in the low-frequency portion of the spectrum. 10 As a result, a deep insight is being gained into the physical mechanisms responsible for superfluidity in doped He clusters and nanodroplets and its manifestation in their rotational spectrum, in terms of the interplay between structure and dynamics, localization, and tunneling. 9 The main theoretical tool employed in these investigations is the dipole-dipole imaginary- time correlation function (CF), whose inverse Laplace transform (ILT) displays peaks in correspondence to dipole-allowed electromagnetic transitions, with strengths proportional to the transition matrix elements between the ground and the excited states. Imaginary-time CFs are easily accessible to reptation quantum Monte Carlo (RQMC) simulations without any other systematic biases than those due to the use of a finite time step and propagation time. 10 The main effect of the residual interactions between the effective rotor and the rest of the host is that the spectrum is not entirely exhausted by the renormalized J ) 1 molecular rotation, thus indicating the presence of additional, weaker spectral features higher in energy. The strength of these additional features, however, may be so weak as to make them hardly detectable through the numerically instable and ill-conditioned ILT operation. The main purpose of this work is to show how the use of generalized, symmetry- adapted, imaginary-time correlation functions allows one to selectively enhance the weight of faint spectral features, thus making them accessible to the analysis of the ILT. As a demonstration of our methodology, we apply it to the He-CO dimer, for which exact diagonalization results are available, and we present preliminary results for the simulation of the satellite band recently observed in the IR spectrum of the CO 2 molecule solvated in He nanodroplets. 12 The absorption spectrum of a molecule embedded in a matrix of helium atoms is given by the Fourier transform of the time autocorrelation of its dipole d. At zero temperature, one has † Part of the “Giacinto Scoles Festschrift”. * To whom correspondence should be addressed. E-mail: moroni@ democritos.it. £ E-mail: skrbic@sissa.it. ‡ E-mail: baroni@sissa.it. I(ω) ∼ ∑ i |〈Ψ i |d ˆ |Ψ 0 〉| 2 δ(E i - E 0 - ω) ) ∫ 〈d ˆ (t)‚d ˆ (0)〉 0 e iωt dt (1) 12749 J. Phys. Chem. A 2007, 111, 12749-12753 10.1021/jp076193v CCC: $37.00 © 2007 American Chemical Society Published on Web 11/09/2007