- #1
grunf
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I have one question about wave functions and molecular orbitals (MO). In the computational quantum chemistry scientists often use Linear Combination Atomic Orbitals (LCAO) to construct MO.
\varphi_{i\lambda\alpha}(\vec{r})=<br /> \sum\limits_{p=1}^{N}\chi_{p\lambda\alpha}(\vec{r})<br /> C_{i\lambda p},
where
\chi_{p\lambda\alpha}(\vec{r})=2^{-1/2}<br /> \left[\chi_{n_{\lambda p} l_{\lambda p}m_{\lambda\alpha}}(\vec{r}_{A})<br /> +\sigma_{\lambda}\chi_{n_{\lambda p} l_{\lambda p}m_{\lambda\alpha}}(\vec{r}_{B})\right].
Here \chi_{n_{\lambda p} l_{\lambda p}m_{\lambda\alpha}}(\vec{r}_{J}) (J=A,B) are the usual Slater-type functions (STF-s) centered on A and B, respectively. \lambda is the symmetry species (\textrm{for example } \sigma or \pi) and \alpha (for example g or u) is the subspecies of symmetry \lambda.
Note, that in the above sum's there is no dependence m_{\lambda\alpha}
from p!?
The question is: Does it means that in some MO (\sigma or \pi, for example) all electrons must have the same magnetic quantum number? Why is that?
Is there some symmetry, some rule, some law or some common property for all electrons in the same MO.
In some papers I have found that for LCAO molecule N_{2} all electrons have
m=0 while in the case of molecule O_{2} m=1. Why is that? Is it possible that some electrons have m=-1?
If somebody have any sugestions about this question, I will be very appreciate.
Regards
\varphi_{i\lambda\alpha}(\vec{r})=<br /> \sum\limits_{p=1}^{N}\chi_{p\lambda\alpha}(\vec{r})<br /> C_{i\lambda p},
where
\chi_{p\lambda\alpha}(\vec{r})=2^{-1/2}<br /> \left[\chi_{n_{\lambda p} l_{\lambda p}m_{\lambda\alpha}}(\vec{r}_{A})<br /> +\sigma_{\lambda}\chi_{n_{\lambda p} l_{\lambda p}m_{\lambda\alpha}}(\vec{r}_{B})\right].
Here \chi_{n_{\lambda p} l_{\lambda p}m_{\lambda\alpha}}(\vec{r}_{J}) (J=A,B) are the usual Slater-type functions (STF-s) centered on A and B, respectively. \lambda is the symmetry species (\textrm{for example } \sigma or \pi) and \alpha (for example g or u) is the subspecies of symmetry \lambda.
Note, that in the above sum's there is no dependence m_{\lambda\alpha}
from p!?
The question is: Does it means that in some MO (\sigma or \pi, for example) all electrons must have the same magnetic quantum number? Why is that?
Is there some symmetry, some rule, some law or some common property for all electrons in the same MO.
In some papers I have found that for LCAO molecule N_{2} all electrons have
m=0 while in the case of molecule O_{2} m=1. Why is that? Is it possible that some electrons have m=-1?
If somebody have any sugestions about this question, I will be very appreciate.
Regards
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