The TEP or trans equatorial propagation is based in the reflection of waves on the F2 layer of the ionosphere, that spreads from 250 to 500 Km of altitude. This layer doesn't reflect VHF signals, even on 50 MHz it does it occasionally and during the periods of highest solar activity.
Then, Why under certain circumstances contacts on 144 MHz can be achieved between stations located approximately at the same longitude, but in opposite hemispheres of the planet?
The maximum frequency reflected by the F2 layer depends of the combination of several factors.
Contacts by single skip are not possible on 144 MHz, because the ionization
never gets so high to allow a signal sent towards the horizon to reach the F2
layer with an attack angle so small that it can be reflected.
Thus we have to search the explanation in the presence of some irregularity (ies) that, always together a high ionization and a small attack angle, allows the signals to be reflected back to the earth instead of losing into the space.
An anomaly that without doubt has influence is know as equatorial anomaly, and it's basically a bend of the ionosphere over the geomagnetic equator. Between 20? north and 20? south of the geomagnetic equator the ionosphere bends forming a protuberance. This happens after sunset (what matches the times of TEP openings) and it seems that is due to the combination of a persistent enlargement of the F layer near the equator and the daily effect of the midday source. This source is apparently the result of the increment of the electric fields from west to east of the equatorial E layer. Combined with the magnetic field of the earth and the ionospheric winds, these fields bomb electrons from the E layer to the lower part of the F upwards, in the higher portion of the F2 layer, with the result of a noticeable increase of the number of electrons in the F2 layer.
This equatorial protuberance has two regions, one at the north and another at the south of the equator and between them the ionosphere is bent upwards. This bending makes that waves reach the border with an attack angle lower that if the layer was spherical and instead of losing into the space they are reflected horizontally till the border of the region of the opposite hemisphere where are reflected again, this time to the earth.. (Notice when I say equator I always mean geomagnetic equator and not geographic)
High enough ionization is necessary on both sides (north and south) of the bent regions. So this condition implies that both hemispheres are equally illuminated, what happens about the equinoxes in autumn and spring when the Sun is over the equator (what completely matches the dates of TEP openings). This model explains the so called afternoon-TEP that allow communications up to 70 MHz, but ionization will never get high enough to support communications on higher frequencies.
Other factors have to be taken into account in order to explain TEP openings on 144 MHz, like a whispering gallery or field-guided mode which relies on the existence of ionospheric bubbles, tubes or plumes that have an electron concentration lower than the surrounding area. Rays are reflected from the surfaces of the bubble walls, at all times staying within the ionosphere until they finally emerge on a path down to the ground.
So, always bear in mind that there are two types of TEP:
Roger Harrison VK2ZRHY, maintain some pages with a very good and detailed explanation of both afternoon TEP and evening TEP, and I also recommend you reading the articles available in the bibliography section.