Minimum dipole moment required to bind an electron to a screened dipole field R. Dı ´ ez Muin ˜ o, 1 M. Alducin, 2 and P. M. Echenique 1,3 1 Donostia International Physics Center (DIPC), Manuel de Lardizabal 4, 20018 San Sebastia ´n, Spain 2 Departamento de Ingenierı ´a Ele ´ctrica, ETSII, UPV/EHU, Alameda de Urquijo, 48013 Bilbao, Spain 3 Departamento de Fı ´sica de Materiales, Facultad de Quı ´micas, UPV/EHU, Apartado 1072, 20080 San Sebastia ´n, Spain Received 27 December 2002; published 14 March 2003 The critical dipole moment required to bind an electron is known since Fermi and Teller published its exact value in a historical contribution E. Fermi and E. Teller, Phys. Rev. 72, 399 1947. We revisit the problem and calculate self-consistently the critical dipole moment for a dipole field embedded in a homogeneous polarizable medium. We show that, although the capability of polar systems to capture electrons in the dipole field is much reduced by the screening, a screened dipole field is still attractive enough to bind one electron for a wide range of embedding media. DOI: 10.1103/PhysRevB.67.121101 PACS numbers: 71.10.Ca, 71.15.Mb, 71.55.-i, 73.20.-r The appearance of bound states for an electron in a dipole field is a problem of central importance in molecular and condensed-matter physics. The history of the research on the subject is appealing as well. In 1947, Fermi and Teller were the first to publish the value of the minimum dipole moment required to bind an electron also known in the literature as the critical dipole moment, namely D min 0 =0.639 a.u. 1 This value was given in their paper in passing, without further mention of it. The actual method that they used to obtain it still remains unclear, and was the subject of an interesting search by Turner. 2 Later works rediscovered the dipole criti- cal value using several methods 3–5 in the context of low- energy electron scattering in polar molecules. After these pioneering studies, and for more than two de- cades, literature on the problem was scarce. In the past few years, however, the concept of the minimum dipole required to bind an electron has been recovered and widely used in the study of dipole-bound anions, to which much theoretical and experimental work has been dedicated. 6–9 Dipole-bound anions are negatively charged molecular compounds in which the binding of the outer electron can be basically in- terpreted in terms of the dipole field of the neutral molecule. The concept of the critical dipole moment is used in this context to predict the existence of such molecular anions. Higher multipole-bound anions have been studied as well. 10 The problem of the critical dipole also reappeared in a quite different context recently: Camblong et al. showed that the binding of an electron to a polar molecule is the realization of a quantum anomaly. 11 Less attention has been paid, however, to the binding of electrons to dipolar fields screened by an external electronic density, which is the relevant situation in condensed matter. Screened dipole fields appear, for example, in metal- semiconductor junctions, 12 liquid-solid interfaces between polar solvents and metals, 13 and heterogeneous interfaces in which nanoparticles are formed. 14 Polar defects stabilized by electron capture were also proposed as responsible for polar- ization fatigue in ferroelectric materials. 15 In surface chem- istry, the screening of polar structures appears in problems such as the adsorption of small polar molecules on metal surfaces. 16 The electronic properties of such systems would be very much affected by the binding of electrons in the dipole field. Our purpose in this paper is to determine the appropriate conditions under which this binding can take place. The screening effect of an external electronic charge into a dipole field implies that higher dipole moments are re- quired to bind one electron. In this paper, we focus our at- tention on such a problem by calculating the critical dipole moment required to bind one electron when a finite dipole is embedded in a jellium. This model is useful to understand the complex mechanisms of electron binding by screened dipole fields and provides an estimate of the actual dipole fields required to bind electrons in real systems. The binding of electrons by a screened dipole was pre- liminarily studied using linear theory of screening Thomas- Fermi potentials and a variational approach for the electron wave function. 17,18 It is well known, however, that linear theory underestimates the rearrangement of electronic charge induced by a charged particle in a homogeneous medium. 19 Hence, we calculate the embedding of a dipole in a jellium using density-functional theory DFT. The screening of the dipole by the external electronic density and the critical di- pole moment are thus obtained in a self-consistent way and beyond linear theory. For the sake of comparison, we will also show the results obtained in linear theory of screening. The inclusion of nonlinearity in the description of the screen- ing has important consequences, with two effects of opposite sign competing. The system on which we focus our attention is a finite dipole defined by two point charges q separated by a dis- tance d atomic units are used throughout. The dipole is embedded in a jellium a constant background of positive charge in which the electrons move, whose mean electronic density is n 0 . The electron-density parameter r s is usually defined by the relation 1/n 0 =4  r s 3 /3. D is the dipole mo- ment D =qd . Our goal is to calculate the critical dipole D min , defined as the minimum dipole moment required to bind an electron, as a function of the external electronic density n 0 . We use the Kohn-Sham KS equations to solve the problem: 20  - 1 2  2 +V eff  r   i  r = i  i  r , 1 RAPID COMMUNICATIONS PHYSICAL REVIEW B 67, 121101R2003 0163-1829/2003/6712/1211014/$20.00 ©2003 The American Physical Society 67 121101-1