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连忙 and 赶忙 cannot be used in the imperative, although 立刻, 马上 (and also 赶快 and 赶紧) can. Technically, 连忙, 赶忙 denote something that happens fast (now), while 立刻, 马上 denote something that is about to happen (soon). See 连忙 as present tense, and 马上 as the future tense, if you will. Imperatives then belong to future actions.
Consider: 贬义词: derogatory term; pejorative -(ABC) derogatory term; expression of censure -(A Chinese English Dictionaty) 两岸 lists a defintion with some examples of these 贬义词: 帶有否定、厭惡等感情色彩的詞（與「褒義詞」相對）。如「昏庸」、「卑鄙」、「討厭」等。也作「貶詞」。 and an example of usage: ‘爱情’二字在他的特别词典里是个贬义词, 跟‘贪污’、‘盗窃’、‘资本主义’等词语一样的难听。 -(周克芹 《许茂和他的女儿们》第四章)
According to iCIBA: If someone is a negative person, or has a negative attitude, then they are 消极 (xiāo jí), or 悲观 (bēi guān). To say that a word has a negative connotation, you use 负面含义 (fùmiàn hányì), literally, "downside meaning". Thanks to S.Rhee for pointing me to iCIBA, where I was able to find the answer to my own question.
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