Multiconfiguration quantum chemical calculation of geometry and electron properties of Fe 2Si 18 cluster indicates on the predictable change of spin states as a function of the excitation energy beginning from ground state with the total spin S = 4. The charges on the two Fe atoms are quite different as well as the charge distribution on the surrounding Si atoms. Nevertheless the total dipole moment of the cluster is a monotonically decreasing function of the excitation energy and it reaches practically zero value in the first singlet state in which the cluster represents a new version of a quibit system.
Some number of bi-center clusters of the T2Sin type were primarily studied for the transition metals (T = Cr, Mn) [
The search of the two-state systems represents intriguing story in the modern investigations of a quantum computer systems. We mention here the point-like NV defect state in diamond [
The accuracy of multiconfigurational method for the Si subsystem can be demonstrated for Si2 molecule with the ground state configuration
For the subsequent calculations of the Fe2Si18 clusters a special basis set was constructed for the iron atom. The core was treated with the 6-31G(f) basis set to which three additional s, p, and d type Gaussian functions were then added. The exponents of the added functions were optimized with retaining all other functions of the 6-31G(f) basis set. Various methods (ROMP2, MCQDPT [
The calculation scheme looks as following. The total spin S of the Fe2 molecule is equal to S = 4 in the ground state and it can induce some spin polarization effect on the surrounding Si atoms. We performed first UHF calculations to take into account this possibility into the consideration with a sufficiently large value of a spin projection MS = 10 that suppose the presence of 8 unpaired electrons in 3d-shells of both Fe-atoms and 12 ones of spin-polarized Si atoms. The obtained UHF natural orbitals were used as the starting orbitals for the next CASSCF calculation with a single high-spin configuration with S = 10 including 20 singly occupied molecular orbitals (MOs) as active orbitals. The obtained CASSCF MOs were transformed to the canonic form with the use of the GAMESS algorithm procedure. These canonized active MOs were divided into three subsets: 6 orbitals with the lowest orbital energies, 8 orbitals resembling 3d-shell states of iron atoms and 6 orbitals with the highest orbital energies. After that three subsets were used to construct three orbital subspaces of the restricted active space self-consistent field (RASSCF) method. The maximum electronic excitation levels between subspaces were allowed to be 2, for the details see also [
The most laborious part in the calculations is of course the investigation of electronic properties in the first singlet state, its description takes Q = 22065484 determinant functions compared to Q = 295795 determinant functions for the ground S = 4 state. Electronic properties are found to be well understandable, the 8 once occupied MOs are well localized on the two Fe atoms, hence all spin states with S = 4, 3, 2, 1, 0 represent the same electronic configuration. Some number of natural orbitals (NOs) with the occupation numbers n = 2, 1, 0 are represented in the
The most important data are summarized below in the
S = 4 | r(Fe1Si14) = 3.027, r(Fe1Si17) = 3.029, r(Fe1Si15) = 2.578, r(Fe1Si18) = 2.578, r(Fe1Si16) = 2.591, r(Fe1Si19) = 2.591, r(Fe1Si8) = 2.906, r(Fe1Si5) = 2.908, r(Fe1Si3) = 2.951, r(Fe1Si6) = 2.952, r(Fe1Si4) = 2.934, r(Fe1Si7) = 2.933, r(Fe1Fe2) = 2.817, r(Fe2Si8) = 3.535, r(Fe2Si5) = 3.537, r(Fe2Si3) = 2.833, r(Fe2Si6) = 2.834, r(Fe2Si4) = 2.829, r(Fe2Si7) = 2.829, r(Fe2Si20) = 2.768, r(Fe2Si11) = 2.768, r(Fe2Si9) = 2.647, r(Fe2Si12) = 2.648, r(Fe2Si10) = 2.646, r(Fe2Si13) = 2.645 | |
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E = −7725.150016а.е. (0эВ) | q(Fe1) = 1.749, q(Fe2) = 0.889, q(Si14) = 0.306, q(Si17) = 0.308, q(Si15) = −0.432, q(Si18) = −0.433, q(Si16) = −0.422, q(Si19) = −0.420, q(Si8) = −0.003, q(Si5) = −0.002, q(Si3) = −0.284, q(Si6) = −0.282, q(Si4) = −0.298, q(Si7) = −0.300, q(Si20) = 0.162, q(Si11) = 0.163, q(Si9) = −0.175, q(Si12) = −0.176, q(Si10) = −0.175, q(Si13) = −0.174 | |
S = 0 | r(Fe1Si14) = 3.008, r(Fe1Si17) = 3.008, r(Fe1Si15) = 2.581, r(Fe1Si18) = 2.581, r(Fe1Si16) = 2.588, r(Fe1Si19) = 2.588, r(Fe1Si8) = 2.922, r(Fe1Si5) = 2.922, r(Fe1Si3) = 2.974, r(Fe1Si6) = 2.974, r(Fe1Si4) = 2.964, r(Fe1Si7) = 2.964, r(Fe1Fe2) = 2.845, r(Fe2Si8) = 3.546, r(Fe2Si5) = 3.546, r(Fe2Si3) = 2.830, r(Fe2Si6) = 2.830, r(Fe2Si4) = 2.839, r(Fe2Si7) = 2.839, r(Fe2Si20) = 2.769, r(Fe2Si11) = 2.769, r(Fe2Si9) = 2.648, r(Fe2Si12) = 2.648, r(Fe2Si10) = 2.645, r(Fe2Si13) = 2.645 | |
E = −7725.147837а.е. (0.059эВ) | q(Fe1) = 1.723, q(Fe2) = 0.816, q(Si14) = 0.293, q(Si17) = 0.293, q(Si15) = −0.415, q(Si18) = −0.415, q(Si16) = −0.430, q(Si19) = −0.430, q(Si8) = 0.032, q(Si5) = 0.032, q(Si3) = −0.302, q(Si6) = −0.302, q(Si4) = −0.294, q(Si7) = −0.294, q(Si20) = 0.171, q(Si11) = 0.171, q(Si9) = −0.161, q(Si12) = −0.161, q(Si10) = −0.165, q(Si13) = −0.165 |
NO #143 n = 1.997 | NO #151 n = 1.012 | NO #154 n = 1.000 | NO #162 n = 0.005 |
NO #143 n = 1.999 | NO #154 n = 0.993 | NO #155 n = 0.950 | NO #162 n = 0.004 |
Spin number | Δq (e) | ΔΕ (eV) | |
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S = 0 | 0.005 | 0.907 | 0.059 |
S = 1 | 0.012 | 0.900 | 0.056 |
S = 2 | 0.033 | 0.886 | 0.048 |
S = 3 | 0.059 | 0.883 | 0.033 |
S = 4 | 0.124 | 0.860 | 0.000 |
We conclude: 1) the excitation energy between neighboring spin states is a decreasing function of the transition energy, 2) the charge difference Δq is nearly stable, 3) the total dipole moment is a drastically decreasing function of the transition energy ΔΕ. The last observation is most importance and it can be understood as following. The large positive charge on one Fe-atom, it denoted by number 1 in the
The symmetric charge distribution is unstable, there arise some kind of “up and down states” in the sense of the charge distribution in the degenerate electronic state. This conclusion can be checked by the measurement of Mössbauer spectra on the two Fe-atoms. Only the stable electronic structures were described above, the problem of their transformations is to be discussed separately.
S = 3 | S = 2 | S = 1 |
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E = −7725.148819 ΔΕ = 0.033 | E = −7725.148235 ΔΕ = 0.048 | E = −7725.147953 ΔΕ = 0.056 |
r(Fe1Si14) = 3.030, r(Fe1Si17) = 3.021, r(Fe1Si15) = 2.579, r(Fe1Si18) = 2.579, r(Fe1Si16) = 2.590, r(Fe1Si19) = 2.590, r(Fe1Si8) = 2.913, r(Fe1Si5) = 2.914, r(Fe1Si3) = 2.962, r(Fe1Si6) = 2.962, r(Fe1Si4) = 2.947, r(Fe1Si7) = 2.946, r(Fe1Fe2) = 2.827, r(Fe2Si8) = 3.539, r(Fe2Si5) = 3.539, r(Fe2Si3) = 2.834, r(Fe2Si6) = 2.834, r(Fe2Si4) = 2.831, r(Fe2Si7) = 2.831, r(Fe2Si20) = 2.769, r(Fe2Si11) = 2.769, r(Fe2Si9) = 2.647, r(Fe2Si12) = 2.647, r(Fe2Si10) = 2.645, r(Fe2Si13) = 2.645 | r(Fe1Si14) = 3.009, r(Fe1Si17) = 3.009, r(Fe1Si15) = 2.580, r(Fe1Si18) = 2.580, r(Fe1Si16) = 2.589, r(Fe1Si19) = 2.589, r(Fe1Si8) = 2.919, r(Fe1Si5) = 2.919, r(Fe1Si3) = 2.974, r(Fe1Si6) = 2.974, r(Fe1Si4) = 2.962, r(Fe1Si7) = 2.961, r(Fe1Fe2) = 2.845, r(Fe2Si8) = 3.539, r(Fe2Si5) = 3.539, r(Fe2Si3) = 2.831, r(Fe2Si6) = 2.831, r(Fe2Si4) = 2.832, r(Fe2Si7) = 2.832, r(Fe2Si20) = 2.770, r(Fe2Si11) = 2.770, r(Fe2Si9) = 2.648, r(Fe2Si12) = 2.648, r(Fe2Si10) = 2.646, r(Fe2Si13) = 2.646 | r(Fe1Si14) = 3.009, r(Fe1Si17) = 3.009, r(Fe1Si15) = 2.581, r(Fe1Si18) = 2.581, r(Fe1Si16) = 2.588, r(Fe1Si19) = 2.588, r(Fe1Si8) = 2.921, r(Fe1Si5) = 2.921, r(Fe1Si3) = 2.973, r(Fe1Si6) = 2.973, r(Fe1Si4) = 2.963, r(Fe1Si7) = 2.963, r(Fe1Fe2) = 2.846, r(Fe2Si8) = 3.545, r(Fe2Si5) = 3.545, r(Fe2Si3) = 2.831, r(Fe2Si6) = 2.831, r(Fe2Si4) = 2.838, r(Fe2Si7) = 2.838, r(Fe2Si20) = 2.769, r(Fe2Si11) = 2.769, r(Fe2Si9) = 2.647, r(Fe2Si12) = 2.647, r(Fe2Si10) = 2.645, r(Fe2Si13) = 2.644 |
q(Fe1) = 1.738, q(Fe2) = 0.855, q(Si14) = 0.301, q(Si17) = 0.302, q(Si15) = −0.428, q(Si18) = −0.429, q(Si16) = −0.423, q(Si19) = −0.422, q(Si8) = 0.012, q(Si5) = 0.012, q(Si3) = −0.289, q(Si6) = −0.288, q(Si4) = −0.298, q(Si7) = −0.299, q(Si20) = 0.166, q(Si11) = 0.167, q(Si9) = −0.169, q(Si12) = −0.170, q(Si10) = −0.170, q(Si13) = −0.169 | q(Fe1) = 1.720, q(Fe2) = 0.834, q(Si14) = 0.293, q(Si17) = 0.293, q(Si15) = −0.424, q(Si18) = −0.424, q(Si16) = −0.426, q(Si19) = −0.426, q(Si8) = 0.027, q(Si5) = 0.027, q(Si3) = −0.291, q(Si6) = −0.291, q(Si4) = −0.293, q(Si7) = −0.294, q(Si20) = 0.168, q(Si11) = 0.168, q(Si9) = −0.165, q(Si12) = −0.165, q(Si10) = −0.167, q(Si13) = −0.166 | q(Fe1) = 1.721, q(Fe2) = 0.821, q(Si14) = 0.293, q(Si17) = 0.293, q(Si15) = −0.416, q(Si18) = −0.416, q(Si16) = −0.429, q(Si19) = −0.429, q(Si8) = 0.031, q(Si5) = 0.031, q(Si3) = −0.300, q(Si6) = −0.300, q(Si4) = −0.294, q(Si7) = −0.294, q(Si20) = 0.170, q(Si11) = 0.170, q(Si9) = −0.162, q(Si12) = −0.162, q(Si10) = −0.165, q(Si13) = −0.165 |