In school I learned that adverbs can modify verbs, adjective, or other adverbs. Never did I hear the term “sentence adverbs”, and it was only recently that I first heard of this concept.
As the name suggests, it is an adverb that modifies the whole sentence, and not a particular word in the sentence. An example is, “Fortunately, Hurricane Isaac missed Tampa and the GOP convention was able to proceed with its business last week. Unfortunately, all decisions had already been made beforehand, and there was no real business to conduct.”
Here the adverbs “fortunately and “unfortunately” are used as sentence adverbs, modifying the whole thought. One could use “It is fortunate that”, or “I think it is fortunate that”, instead of “fortunately”, but obviously the use of one word is preferable to the longer and more awkward phrase that would be needed as a substitute.
So far so good. But the problem comes in when such words are used improperly. A news anchor said “X allegedly killed Y.” Here the use of “allegedly” right before the verb makes it look like it is the verb that is being modified, and this makes no sense, for one cannot be “allegedly killed”. “Allegedly” here is being used as a sentence adverb, and needs to be set off with a comma (if at the beginning of the sentence), or two (if in the middle).
An even worse misuse of “allegedly” occurred in a news report which stated that “X was being charged with allegedly killing Y”. This is total nonsense; X was not being charged with allegedly killing Y, he was being charged with killing Y. The concept of “allegedly” is contained in the verb “charged”, and no further modification is necessary or at all useful. News people seem to be so obsessed with being politically correct that they continue to make these glaring errors.
The number one problem in this area is of course the word “hopefully”, whose careless use is widely castigated. I could say, “Hopefully, you will find this explanation of sentence adverbs helpful”. The problem here is that “hopefully” does not modify anything found in the sentence; it is thrown into the mix solely to convey the writer’s point of view. It is not a real adverb here, and should be replaced with “I hope”, or something similar.
(Some may complain that “hopefully” is a weasel word, in which the writer of speaker uses the passive voice in order to avoid responsibility for the matter at hand. An example is when a president responds to a scandal in his administration, as Reagan once did, by saying “Mistakes were made”. But this is not the real crux of the problem with ”hopefully”.)
While some grammarians have come to accept the use of “hopefully”, the best advice is still to avoid it unless you know your audience is accepting of such casual use of the language. One need not resort to awkward and wooden alternatives like “It is to be hoped”, or “One hopes”, as there are more natural-sounding options available like “Let’s hope”, or “With luck”. Let's hope you can learn to use them instead.