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Using response methods at the RPA level we have calculated mean excitation energies of the 3d-elements and all their cations. We have shown that the dependence of mean excitation energies of the cations on the number of electrons is nearly the same for all 3d-elements. Using a quadratic Z-dependence of mean excitation energies in isoelectronic series, we have estimated mean excitation energies of some of the more highly charged cations of K, Ca, Ga, Ge, As, Se, Br and Kr. Also estimated values for the mean excitation energies of singly, negatively charged ions of 3d-elements are reported. We have shown how to calculate orbital mean excitation energies for the 3datoms from the mean excitation energy of their cations.

We have investigated the relationship between two methods to obtain mean excitation energies of large samples using a modified Bragg rule, one method using Bragg’s rule to determine elemental mean excitation energies from experimental stopping power data, and another method going the opposite way, that is determining compound mean excitation energies from theoretical elemental mean excitation energies and bond correction factors. We show how to obtain bond correction factors from elemental mean excitation energies and vice versa. The comparison leads to insight into the importance of the effect of chemical binding on the experimentally determined elemental mean excitation energies. We also introduce the concept of atomic correction factor that links theoretical, gas phase atomic mean excitation energies to elemental mean excitation energies.

We report bond correction factors that can be used to calculate molecular mean excitation energies including the effects of chemical bonding. The calculations are based on an extension of Bragg’s rule. We report results for several bonds – neutral and charged - involving gas phase atoms in the first, second and third row of the periodic system. The bond correction factors are dimensionless and turn out to be nearly constant and of the order 1-2. The method is applied to the calculations of mean excitation energies of linear hydrocarbons, amino acids and molecules and molecular ions of astrophysical interest. Examples show that chemical binding effects increase the molecular mean excitation energies with between 4 % to 15 %, smallest for linear, unsaturated molecules and largest for molecules with longer aliphatic chains.

We present hitherto unknown mean excitation energies of singly charges atomic anions with Z≤ 18. Most of them are calculated using the Random-phase Approximation and large basis sets. We have shown that there is a nearly Z-independent, constant ratio between the mean excitation of anions and atoms. We have also shown that Bragg’s rule may be applied to determine the mean excitation energies of negative ions from mean excitation energies of atoms and cations with same nuclear charge but different number of electrons. These relationships were then used to estimate the mean excitation energies of the anions that we could not calculate directly.

The purpose of this paper is to identify the fragmentation patterns of molecules and ions that give the best fulfilment of a Bragg’s rule estimation of the mean excitation energy of the molecules and ions. We investigate the effect of chemical binding on the validity of Bragg’s rule for the calculation of stopping cross sections and mean excitation energies. As test cases we use a series of small molecules and molecular ions, primarily carbon and nitrogen halides. We are using several nuclear fragments of the same molecule or ion to test the dependence of Bragg’s rule on the binding energy of the molecules/ions. The mean excitation energies of the molecules/ions and their fragments are computed with the same method. We find that neglect of chemical binding nearly always results in an underestimation of the mean excitation energies. We also find that the fully atomic decomposition of any molecule but a diatomic molecule never gives the best fulfilment of Bragg’s rule. The best fulfilment of Bragg’s rule is obtained when using a fragmentation pattern with as few bonds as possible broken and when the choice of fragments is guided by chemical knowledge and intuition. By investigating several alternative fragmentation patterns for a molecule/ion, guidelines for choice of optimal Bragg rule fragmentation are suggested. Using the best fragmentation pattern for the tested molecules and ions, the error in the mean excitation energy is of the order of 5 % or less, implying an error of not more than 1 % in the pure Bethe stopping power as a result of applying Bragg’s rule.

We present dipole oscillator strength-dependent properties such as sum rules, dipole polarizability, mean excitation energy, and stopping cross section as a function of the ionic charge of C, F, Si, and Cl atoms. The excitation spectra and the dipole oscillator strengths are obtained by means of the time-dependent Hartree–Fock approximation. We report the sum rules, Sk, from −6 ≤ k ≤ 2 and the logarithmic sum rule Lk = dSk/dk as a function of the ionic charge −1 ≤ q ≤ Z − 1 with Z being the nuclear charge. The contributions from the bound and continuum states to all sum rules are analyzed as a function of k and charge of the cation. The study allows us to determine a scaling behavior of the bound and continuum state contributions in terms of the cation number of electrons and nuclei charge for k ≤ 0. We propose a new way of determining orbital mean excitation energy as the difference between the mean excitation energy of two neighboring cationic states of an atom. This procedure allows to obtain all orbital mean excitation energy for the four atoms within the time-dependent Hartree–Fock approximation, thus effectively including electronic correlation in the orbital mean excitation energy. As a result, the mean excitation energy within a shell differs for each electron. Wherever possible, we compare with available data in the literature finding excellent agreement.

We present a review of calculations of mean excitation energies of small molecules, atoms and their ions using the Random-Phase Approximation. We discuss the relationship with other calculations and we propose several simple rules that may be used to estimate mean excitation energies of cations and singly charged anions. We conclude that the accuracy of the mean excitation energies obtained using this method in terms of choice of basis sets and inclusion of electron correlation is enough to obtain experimental accuracy of stopping powers of gas phase small molecules, atoms and their ions.