This is closer to the truth than it isn't, although this makes it sound like the Japanese high command weren't to blame-which they entirely were.

Before I elaborate, it's worth looking at /u/AsiaExpert 's post, especially the beginning where he says:

The Rape of Nanking is the historian's equivalent of a potential nuclear meltdown in a shoddy home made reactor. Even going near the topic or mentioning it in passing is dangerous territory. The topic is also a magnet for controversy and heated emotions. I usually avoid it because I usually get no where with it.

This is absolutely correct.

To understand why the Japanese sacked Nanjing, we need to understand the command structure and organization of the Imperial Japanese Army. The most important thing to understand is that while the Japanese military was very hierarchical, it also suffered from an inability to tightly corral the action of junior officers. This was due to the utter failure of the Japanese high command-and the government-to rein in and make examples of these junior officers in order to preserve the facade that the Japanese military was perfectly in control. Throughout the 1920s and 1930s, there were numerous incidents of hardline Japanese officers either assassinating politicians, instigating border skirmishes, and otherwise causing trouble, leading up to two important events: the Mukden Incident and the May 15th Incident. Both of these incidents were spurred on by junior officers acting way out of their authority: the former, junior officers essentially unilaterally invading Manchuria, the latter, junior officers assassinating the Prime Minister of Japan. Neither of these incidents were punished harshly: the former officers were even promoted for their audacity, while the latter officers had popular support and received minor prison sentences. With these kinds of incentives, this created the perverse situation where an effort to play down the insubordination problem in the Japanese military resulted in an intensification of the insubordination. This resulted in an idea of gekokujo, a concept dating from the Japanese Sengoku Era where real political power is controlled by figures lower in the formal hierarchy, rather than in the nominal ruler.

Things appeared to come to a head in the wake of the 2-26 incident, where a group of junior officers attempted to start a coup to overthrow the government. Unlike the previous incidents, this incident was harshly punished, but the civilian government, in fear of further coup attempts, essentially ceded power to the military in hopes of avoiding an actual successful coup. The same military that had so far been completely unable to keep their junior officers in line. And this was in peace time: in a combat situation the problem was even worse, with several battles in China where Japanese commanders seeking glory would end up attacking Chinese positions against orders and on some occasions launching attacks without supporting units that inevitably failed or resulted in heavier casualties than were necessary.

So, we have demonstrated so far that the high command was unable-or willing-to attempt to control its junior officers. But what was to stop the enlisted and NCOs from similarly breaking free of the control of the junior officers? The answer is simple: the disciplinary system of the Japanese military.

Despite numerous attempts at reform, the Japanese military relied heavily on one key tool to maintain discipline in its ranks: physical violence. Lieutenants would beat up NCOs, who would beat up privates and other enlisted, who in turn had their own hierarchy of senior to junior, Japanese to non-Japanese, that they would beat up in turn. These beatings sometimes happened in the higher ranks too: Tamon Yamaguchi, a senior admiral, once put another admiral in a judo hold in an attempt to have his way. Whatever the causes, the fact that violence was generally accepted as a means of maintaining order resulted in a situation where common soldiers had no qualms about using violence on anyone considered inferior to them. And if you were at the bottom of the totem pole-say, a Korean conscript, for instance-everybody would be beating you up, and you would have nobody to beat up in turn.

So we now have a situation where we have now seen the behavior of the various classes of the Japanese army:

1. Senior officers are disinclined to punish dissent in the junior officer ranks
2. Junior officers have strong incentives to disobey senior officer orders and to commit "bold actions" (promotion and glory if I succeed, a slap on the wrist if I am caught)
3. Order is maintained by committing physical violence, with a large group of frustrated conscripts that have nobody to vent their frustration on at the bottom

Now take this army and place it in the following scenario: you have just spent six months of bloody warfare to finally capture this large capital city, after you were told the war would be over in two weeks. Many of your friends have been killed or wounded. There are still some snipers and other fighters hiding somewhere in the city. You now face a hostile, foreign, civilian populace and a large number of surrendered prisoners, the same ones that have been fighting you for the past six months and are sniping at you here and there. And just for shiggles, the commanding general has done his best to try and slow down your advance at every turn (something about "outstretched supply lines" or something, who cares?), and you have no respect for him. Oh, and he got sick with malaria.

What do you think will happen?

There's always more to be said! But in the meantime, you might be interested in a couple of earlier answers on the subject:

• During the second Sino-Japanese war, was the "Rape of Nanking" conducted as a policy direction from the Japanese Officers or had they lost control of their Enlisted men? - by /u/AsiaExpert, which discusses multiple perspectives in a complex debate

• Why was The Empire of Japan particually vicious during WW2 , or is it due to propaganda that people think that? - by /u/ParkSungJun, which sets Nanking in a broader context

Broadly speaking, the war crimes commited in the Nanking massacre can be divied into two types:

: Violence against civilians (murder, rape, arsoning, looting)

: Mass execution of POWs

The former is pretty much what the OP described; exhausted, vengeful Japanese troops with a strong hatred towards the Chinese people went into a pscyhotic frenzy with the city's fall. They then went on a rampage against the local population, with the commanders not really doing anything to stop them. Such behaviors were prohibited under the rules of engagments set up by the Japanese expeditionary force HQ, but it had zero effect in stopping the troops and in the end the high command did very little to stop them.

The latter is more tricky. While it is debatable whether if the high command of the Japanese expeditionary force like Matsui explicitly had a policy of taking no prisoners, there certainly was such a policy among several division-level commanders.

In December 13th, right after the fall of Nanking, lieutenant-general Yanagikawa Heisuke of the 10th army issued the following order: "The 10th army is to utterly annihilate the enemy inside the walls of Nanking. Every necessary measures are to be taken for this including bombardment and if necessary, arsoning. Do not be deceived by enemy deceptions". Such indiscriminate policy was in fact a violation of the rules of engagement set up by the Japanese expeditionary force HQ, but this order clearly encouraged the Japanese troops to commit war crimes.

On division-level, mass execution of POWs were done in an organized manner. Major-general Akiyama Yoshimitsu of the 6th brigade, 9th division issued the following order: "Since most of the fleeing enemy is now believed to be in plain-cloths, anyone suspected of being so is to be apprehended and housed in appropriate location. Consider every young men to be either a fleeing enemy or one in plain-cloths, and they must all be apprehended".

There were two big problems with this apprehension order: the poor logistics of the Japanese army did not allow to take such an enormous amount of prisoners, and many Japanese troops had no intention of taking prisoners in the first place. As result, anyone suspected of being a fleeing nationalist troop or a partiasan was simply executed on spot. Major-general Sasaki Toichi of the 16th division recorded in his diary that thousands of POWs were executed by enraged troops, some even ignoring the direct order of the superiors: an action Sasaki actually condoned, noting that the division had no food to feed those POWs. Indeed, the whole 16th division had a policy of not taking any prisoners: something cleary stated by lieutenant-general Nakajima Kesago, the commander of the said division, in his diary entry of December 13th. Nakajima states that the division had a policy of no prisoners. He was fearful that the sheer numbers of POWs may induce them to start a desparate riot against their captors, so he readied multiple trucks and sent the POW in many small groups to various locations, executing one group at a time. The division "disposed" at least 23,000 POWs in that day alone.

The "search" for nationalist troops in plain-cloths were extremely shoddy as well, decided on a whim of invidiual soldiers. The decision was based on such vague factors like the way a man walked, or even if a man had a "facial expression of a soldier". If a person was determined to be a plain-clothed troop, then that person was promptly executed without any trial. Therefore it is certain that many of the executed "POW" actually included civilians mistaken to be nationalist troops.

So the conclusion: it is probably true that the high-command of the Japanese expeditionary force only became aware of the scale of barbarity exhibited by the Japanese troops after they entered Nanking several days after the city's fall. But obviously, divisional commanders on the front line would have been well-aware of the situation the moment the city fell, and they did not seem to have done anything to stop the troops from going on a rampage. The "take no prisoners" order they issued definitely encouraged the troops to commit war crimes as well.

The mass executions of POWs, which would certainly have included large numbers of civilians mistaken to be fleeing nationalist troops, was another matter. This was an organized effort by the Japanese army, at least on divisional level, with full consent and orders from its commanders. This certainly was not a case of small groups of soldiers acting against orders: the executions were commited as a military operation.

Source:

: 笠原十九司『南京事件』（岩波書店、1997）Kasahara Tokushi, The Nanking Incident, (Iwanami-Shoten, 1997)