Table 1 The main contributions to the spectral intensity for Kα and 3a1 IRD for the symmetric \({{{{\rm{M}}}}}^{q}{[{{\mbox{H}}}_{2}{\mbox{O}}]}_{6}\) model, with Mq = Na+ and Mg2+, in atomic units

From: Non-local X-ray intermolecular radiative decay probes solvation shell of ions in water

Metal atom

Na

Mg

Transition

 

Kα

IRD 3a1

 

Kα

IRD 3a1

 

tν

\({C}_{{{{\rm{M}}}}2p}^{\nu }\)

\({{{{\rm{t}}}}}_{\nu }{C}_{{{{\rm{M}}}}2p}^{\nu }\)

\({C}_{3{{\rm{a}}}_{1}}^{\nu }\)

\({{{{\rm{t}}}}}_{\nu }{C}_{3{{\rm{a}}}_{1}}^{\nu }\)

tν

\({C}_{{{{\rm{M}}}}2p}^{\nu }\)

t\({}_{\nu }{C}_{{{{\rm{M}}}}2p}^{\nu }\)

\({C}_{3{{\rm{a}}}_{1}}^{\nu }\)

\({{{{\rm{t}}}}}_{\nu }{C}_{3{{\rm{a}}}_{1}}^{\nu }\)

Atomic orbital ν

× 10−3

 

× 10−3

 

× 10−3

× 10−3

 

× 10−3

 

× 10−3

M 2p

49.11

0.97

47.6

0.08

3.93

47.05

0.99

46.6

0.03

1.41

M 3p

−4.53

0.01

−0.045

−0.08

0.362

−6.78

−0.01

0.068

−0.35

2.37

M 4p

0.45

−0.02

−0.009

0.11

0.049

0.93

0.01

0.009

0.18

0.167

O 2p

0.04

0.00

0.002

0.81

0.032

0.06

0.00

0.047

0.79

0.047

Tμ2 × 10−6

2405.99

17.39

 

2216.23

14.74

  1. The considered value of the M-O distance R was 2.3 Å for Na and 2.1 Å for Mg. In the columns, tν denotes the respective symmetry-allowed Cartesian component of the atomic dipole transition moments tM1s,ν (a. u.) and \({C}_{\mu }^{\nu }\) denotes the orbital coefficient of the main atomic orbitals ν in the LCAO description of the hybrid orbitals ψμ. In the bottom row, Tμ2 = \(| {\sum }_{\nu }{{{{\bf{t}}}}}_{\nu }{C}_{\mu }^{\nu }{| }^{2}\) is proportional to the total spectral intensity of the Kα and 3a1 IRD transitions. Note that Tμ2 also includes minor contributions from M np orbitals with n larger than 4. Data are from molecular orbitals optimized for the ground state by HF.