Leaders of war: modelling the evolution of conflict among heterogeneous groups.

War, in human and animal societies, can be extremely costly but can also offer significant benefits to the victorious group. We might expect groups to go into battle when the potential benefits of victory (V) outweigh the costs of escalated conflict (C); however, V and C are unlikely to be distributed evenly in heterogeneous groups. For example, some leaders who make the decision to go to war may monopolize the benefits at little cost to themselves ('exploitative' leaders). By contrast, other leaders may willingly pay increased costs, above and beyond their share of V ('heroic' leaders). We investigated conflict initiation and conflict participation in an ecological model where single-leader-multiple-follower groups came into conflict over natural resources. We found that small group size, low migration rate and frequent interaction between groups increased intergroup competition and the evolution of 'exploitative' leadership, while converse patterns favoured increased intragroup competition and the emergence of 'heroic' leaders. We also found evidence of an alternative leader/follower 'shared effort' outcome. Parameters that favoured high contributing 'heroic' leaders, and low contributing followers, facilitated transitions to more peaceful outcomes. We outline and discuss the key testable predictions of our model for empiricists studying intergroup conflict in humans and animals. This article is part of the theme issue 'Intergroup conflict across taxa'.

A single molecule as a dielectric medium.

For three molecules with weak or negligible charge overlap, we prove that the three-body interaction energy obtained from quantum perturbation theory (to leading order) fits a dielectric model with a nonlocal electronic screening function. The electronic charge cloud of each molecule acts as a dielectric medium for the interaction of the remaining two with the nonlocal dielectric function epsilon(r,r') obtained by O. S. Jenkins and K. L. C. Hunt [J. Chem. Phys. 119, 8250 (2003)], by considering the charge redistribution induced in a single molecule by an external perturbation. The dielectric function depends parametrically on the coordinates of the nuclei, within the Born-Oppenheimer approximation. We also prove that the force on each nucleus in molecule A depends on intramolecular dielectric screening within A. The potential from the charge distribution of B, screened by C acting as a dielectric medium, is further screened linearly within A; and similarly, with the roles of B and C reversed. In addition, the potential due to the unperturbed charge distribution of B and the potential due to the unperturbed charge distribution of C, acting simultaneously, are screened nonlinearly within A. The results show that nonlocal dielectric theory holds on the molecular level, provided that the overlap of the electronic charge distributions is weak.

Roto-translational Raman spectra of pairs of hydrogen molecules from first principles.

We calculate the collision-induced, roto-translational, polarized, and depolarized Raman spectra of pairs of H(2) molecules. The Schrodinger equation of H(2)-H(2) scattering in the presence of a weak radiation field is integrated in the close-coupled scheme. This permits the accounting for the anisotropy of the intermolecular potential energy surface and thereby it includes mixing of polarizability components. The static polarizability invariants, trace and anisotropy, of two interacting H(2) molecules were obtained elsewhere [Li et al., J. Chem. Phys. 126, 214302 (2007)] from first principles. Here we report the associated spherical tensor components which, along with the potential surface, are input in the calculation of the supramolecular Raman spectra. Special attention is paid to the interferences in the wings of the rotational S(0)(0) and S(0)(1) lines of the H(2) molecule. The calculated Raman pair spectra show reasonable consistency with existing measurements of the polarized and depolarized Raman spectra of pairs of H(2) molecules.

The collision-induced polarizability of a pair of hydrogen molecules.

Collision-induced light scattering, impulsive stimulated scattering, and subpicosecond-induced birefringence all depend on the transient changes Deltaalpha in molecular polarizabilities that occur when molecules collide. Ab initio results for Deltaalpha are needed to permit comparisons with accurate experimental results for these spectra and for refractive index virial coefficients and dielectric virial coefficients. In this work, we provide results for Deltaalpha for a pair of hydrogen molecules, treated at CCSD(T) level, with an aug-cc-pV5Z (spdf) basis set. Our values replace the best previous ab initio results for the variation of Deltaalpha with intermolecular separation, the self-consistent-field results obtained by Bounds [Mol. Phys. 38, 2099 (1979)] with a relatively small (3s2p) basis set for H2. For the six geometrical configurations studied by Bounds, the inclusion of correlation and improvements in the basis tend to increase both the trace Deltaalpha(0)0 and the anisotropy Deltaalpha2m of the pair polarizability. The change in the anisotropy is relatively small, but our values for the trace differ by factors of 2 or more from Bounds' results. For use in computing experimental line shapes, intensities, and virial coefficients, we have calculated Deltaalpha for 18 different relative orientations of a pair of H2 molecules, with the intermolecular separation R ranging from 2 a.u. (3 a.u. for a linear pair) to 10 a.u. The H2 bond length is fixed at the vibrationally averaged internuclear separation in the ground state r=1.449 a.u. Our results agree well with the CCSD(T) results for Deltaalpha obtained by Maroulis [J. Phys. Chem. A 104, 4772 (2000)] for two pair configurations of H2...H2 (linear and T-shaped) at a fixed internuclear distance of R=6.5 a.u. in a [6s4p1d] basis. As the intermolecular distance increases (for R>or=8 a.u.), the spherical-tensor components of Deltaalpha converge to the results from a long-range model that includes dipole-induced-dipole (DID) interactions, higher-multipole induction, nonuniformity of the local field, hyperpolarization, and van der Waals dispersion. Deviations from the first-order DID model are still evident for R between 8 and 10 a.u. in most orientations of the pair. At shorter range, overlap damping, exchange, and orbital distortion reduce both Deltaalpha0(0) and Deltaalpha(2)0 below their long-range limiting forms.

Far-infrared absorption by collisionally interacting nitrogen and methane molecules.

Quantum line shape calculations of the rototranslational enhancement spectra of nitrogen-methane gaseous mixtures are reported. The calculations are based on a recent theoretical dipole function for interacting N(2) and CH(4) molecules, which accounts for the long-range induction mechanisms: multipolar inductions and dispersion force-induced dipoles. Multipolar induction alone was often found to approximate the actual dipole surfaces of pairs of interacting linear molecules reasonably well. However, in the case of the N(2)-CH(4) pair, the absorption spectra calculated with such a dipole function still show a substantial intensity defect at the high frequencies (>250 cm(-1)) when compared to existing measurements at temperatures from 126 to 297 K, much as was previously reported.