Python pandas convert datetime to timestamp effectively through dt accessor

I think you need convert first to numpy array by values and cast to int64 - output is in ns, so need divide by 10 ** 9:

df['ts'] = df.datetime.values.astype(np.int64) // 10 ** 9
print (df)
              datetime          ts
0  2016-01-01 00:00:01  1451606401
1  2016-01-01 01:00:01  1451610001
2  2016-01-01 02:00:01  1451613601
3  2016-01-01 03:00:01  1451617201
4  2016-01-01 04:00:01  1451620801
5  2016-01-01 05:00:01  1451624401
6  2016-01-01 06:00:01  1451628001
7  2016-01-01 07:00:01  1451631601
8  2016-01-01 08:00:01  1451635201
9  2016-01-01 09:00:01  1451638801
10 2016-01-01 10:00:01  1451642401
11 2016-01-01 11:00:01  1451646001
12 2016-01-01 12:00:01  1451649601
13 2016-01-01 13:00:01  1451653201
14 2016-01-01 14:00:01  1451656801
15 2016-01-01 15:00:01  1451660401
16 2016-01-01 16:00:01  1451664001
17 2016-01-01 17:00:01  1451667601
18 2016-01-01 18:00:01  1451671201
19 2016-01-01 19:00:01  1451674801
20 2016-01-01 20:00:01  1451678401
21 2016-01-01 21:00:01  1451682001
22 2016-01-01 22:00:01  1451685601
23 2016-01-01 23:00:01  1451689201
24 2016-01-02 00:00:01  1451692801

to_timestamp is used for converting from period to datetime index.

I think you should not use apply, simply astype would be fine:

df['ts'] = df.datetime.astype('int64') // 10**9