Question: ```
summed over all particles \centerline{$\qquad \ddtt\sum_j
m_i\br_i=\sum_i \bF_i+\sum_{\substack {i,j \\ i\neq j}} \bF_{ij}$}

```

[![enter image description here](https://i.stack.imgur.com/0c8r2.png)](https://i.stack.imgur.com/0c8r2.png)

So how to make the second formula centered relative to the whole line rather than to the rest of the line?

Answer: 
Move `\textcircled` inside the `\raisebox` command. As the error message says, `\textcircled` has to be used in text mode, not math mode.

```
\documentclass{article}
\newcommand*\tcircle[1]{%
  \raisebox{-0.5pt}{%
    \textcircled{\fontsize{7pt}{0}\fontfamily{phv}\selectfont #1}%
  }%
}
\begin{document}
\[T_{\tcircle{A},i}-T_1\]
\end{document}

```

[![enter image description here](https://i.stack.imgur.com/dOHfB.png)](https://i.stack.imgur.com/dOHfB.png)
Using a mix of packages including `harmony` and `scalerel` to decrease or increase the text-circle "symbol" to have a good subscript, with this new macro, different from the original of the OP,

```
\newcommand{\lcirc}[1]{\scaleobj{.6}{\mbox{\Kr{#1}}}}

```

you can obtain this MWE:

```
\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{harmony}
\usepackage{scalerel}
\newcommand{\lcirc}[1]{\scaleobj{.6}{\mbox{\Kr{#1}}}}
\begin{document}

\[T_{\lcirc{A},i}-T_1\]
\[T_{\lcirc{a},i}-T_1\]
\[T_{\lcirc{B},i}-T_1\]
\[T_{\lcirc{W},i}-T_1\]
\end{document}

```

... with this output that have the same font into the circle:

[![enter image description here](https://i.stack.imgur.com/eK6Jg.png)](https://i.stack.imgur.com/eK6Jg.png)