Santi Gioacchino e Anna alle Quattro Fontane is a deconsecrated 17th century convent church at Via del Quirinale 24, next door to San Carlo alle Quattro Fontane. Picture of the church on Wikimedia Commons here.
This was originally the friary church of the Spanish reformed Discalced Carmelites, who founded a convent here in 1611. It was their first in Rome as a separate order, as the previously existing Carmelite convents in the city did not accept the reform.
The Carmelite community was expelled by the French after 1798, and it did not return. The friary was abandoned for a short while until granted to a sisterhood, the Perpetual Adorers of the Blessed Sacrament, by Pope Pius VII in 1807. They in turn moved to the nearby church (since demolished) of Santa Maria Maddalena al Quirinale in 1839.
In 1846 the unused convent was attached to the newly founded Belgian College, but in the 1960's this moved to new purpose-built premises at Via Gian Battista Pagano 35 near the Cornelia metro station in the Aurelio district. The church was closed, and it is now formally deconsecrated.
This is a small convent, and the church takes up almost half the floorspace -the college must have found it very cramped. To compensate, the elevation is high, of five storeys The main wing runs along the right hand side of the church, and has a street frontage which occupies the area above the first bays of the church nave. There is another, separate wing behind the apse. Beyond that is a small garden. The left hand wall of the church is also the boundary wall between this convent and that of San Carlo next door, and the cloister of the latter abuts onto it.
The only exterior evidence visible of the church from the street is the doorway. The doorcase is flanked by a pair of half-round Corinthian columns, on high plinths bearing reliefs of lion masks holding wreaths. The columns support an entablature and triangular pediment broken at the top. In the break is inserted a stone cross with a clover-leaf motif on its ends. There is a simple dedicatory inscription between the doorcase lintel and the entablature: Sedente Paulo V SS Ioachim et Annae dic[atum] ("Dedicated to SS Joachim and Anne during the reign of Paul V").
In the aerial photos on the info.roma link you can spot the lantern of the church's shallow dome, with pilasters and a saucer cap in lead. It is completely surrounded by the higher buildings, and is invisible from the ground (the oval dome in the photos is of San Carlo).
The church was designed in a late Baroque style by the architects Paolo Maruscelli and Alessandro Sbrenchio. Despite its unassuming street presence, this is not a very small church and actually has almost twice the floor area of San Carlo.
The overall ground plan is a wide rectangle. At the entrance end the elevation has a nave and aisles with pillared arcades; there are four pillars on each side. Then comes the shallow oval dome, which is supported on two pillars on each side. To make room for this, the aisles are narrowed and the two pairs of pillars set further sideways than the nave arcades. Beyond the dome is a tiny rectangular apse.
The main altar had an anonymous altarpiece of the 17th century showing The Crucifixion. In the cupola of the dome was a fresco of Our Lady of Mount Carmel by Odoardo Vicinelli, and the side chapels were decorated by Pietro Nelli.