MySQL CONVERT_TZ() funciton related issue - php

Question

Below code is used to get last and next Saturday of current week
// GET Last Satuday of current week
$dt_week_start_time = strtotime("last saturday")+((20*3600)+ 1);
$dt_week_start_date = date('Y-m-d G:i:s', $dt_week_start_time);
// GET Last Satuday of current week
$dt_week_end_time = $dt_week_start_time + (7*3600*24) - 1;
$dt_week_end_date = date('Y-m-d G:i:s', $dt_week_end_time);
Below code is used to convert above both date related variables to EST timezone (default timezone is UTC)
$est_time = new DateTimeZone('EST');
$datetime = new DateTime($dt_week_start_date);
$datetime->setTimezone($est_time);
$dt_week_start_date = $datetime->format('Y-m-d G:i:s');
$datetime = new DateTime($dt_week_end_date);
$datetime->setTimezone($est_time);
$dt_week_end_date = $datetime->format('Y-m-d G:i:s');
Now I want to compare these EST timezone dates with dates in mySQL database table. Dates in mySQL database table are stored in UTC timezone by default. By studying on internet and someone suggested to use CONVERT_TZ function. I tried it but it is giving error like mentioned below
What is wrong in my query? Please advise.
Below 2 queries giving this error: 'Notice: Undefined index: purchasedatetime ...'
$str_query_select = "SELECT CONVERT_TZ(purchasedatetime, 'UTC', 'EST' ) FROM t_product_purchase WHERE sellerpkid=1";
$str_query_select = "SELECT CONVERT_TZ((SELECT purchasedatetime FROM t_product_purchase),'UTC','EST') FROM t_product_purchase WHERE sellerpkid=1";