The last few years have been tough on US-China relations, and distrust over long-term intentions has grown on both sides. But now that a new leadership has taken over the reins in China and the Barack Obama administration has started its second term in the US, how can things be set onto a better path? Anything even remotely like a Cold War in Asia would be unwelcome in the region and reduce the possibilities of effectively managing the issues ranging from the Democratic People's Republic of Korea and Iran to climate change.

Presidents Obama and Xi Jinping will meet in California for private talks on June 7-8. This meeting comes amid a stream of high-level Sino-US contacts - Secretary of Treasury Jacob Lew, Secretary of State John Kerry and National Security Advisor Tom Donilon to Beijing, Secretary of Defense Chuck Hagel to the Shangri-La Dialogue, where he met People's Liberation Army representatives, and the Strategic and Economic Dialogue in July in Washington.

But the meeting of the two presidents in California is unique. Never before have American and Chinese leaders sat down outside their respective capitals for a wide-ranging dialogue that will continue for many hours and is not tightly constrained by the requirements of an official visit. The fact that the two leaders have previously spent only 90 minutes with each other - when Xi was still vice-president - makes the meeting all the more significant. And the fact that both are confident enough to have this type of meeting is good news.

One of the most important results of this meeting would be each leader gaining a far better understanding of the other - his key concerns, goals, political considerations and fears. Potentially the most significant take-away from the California meeting would be each leader saying to himself: "I know that person, and I feel confident I can do business with him." Personal chemistry is important in inter-state relations. It determines in part what each judges would be feasible to do with the other. Hopefully, the chemistry between Obama and Xi will be positive.

The key issues on the meeting's agenda are likely to be the DPRK, cyber security, climate change, the Middle East, expansion of military ties and promoting stability in Asia. Bilateral and multilateral economic and trade matters will also come into the mix. Wherever possible, the California meeting should aim to provide direction on how both sides can move beyond what they have done together in the past.

To take just two examples, Washington and Beijing both oppose Pyongyang's nuclear program and both know that the future in the DPRK is uncertain. Yet the US and China have never agreed to discuss concretely the range of potential future scenarios on the Korean Peninsula and their implications. It is time to do so, and the summit should both approve such discussions and mandate that they include both diplomatic and military participants.

On climate change, Washington and Beijing should set aside debates over who bears the greatest responsibility for the current situation and instead focus on concrete, high impact projects and initiatives where the two can cooperate bilaterally and with other high-emission countries to mitigate a threat that confronts us all.

Developing better personal understanding of each other and making progress on how to deal with some major concerns would alone make the summit worthwhile. But there is also a possibility in California to go further.

Both leaders have said that they would like to lay the groundwork for "a new type of major power relations" where, in contrast to the 20th century, the relations between a rising power and the dominant power do not inexorably trend toward conflict. This informal summit provides a unique opportunity for the presidents to discuss candidly what this new concept should mean in practice.

In Beijing, Donilon said the two leaders should discuss the perceptions, interests and priorities guiding their respective approaches to bilateral, regional and global affairs. To be really valuable, this discussion should also specifically address areas in which deeper cooperation can yield disproportionate benefits, as well as candidly determine where fault lines will remain in place. This exchange should adopt a long-term perspective and lead to sustained, high-level dialogue on the core threats that will shape the world of the future - and the potential roles of the US and China separately and collaboratively in such a world.

It is in the context of this type of truly strategic discussion that cooperation on specific issues can lead to greater trust of each other's long-term intentions. The potential upside of this unprecedented US-China meeting is thus substantial if the two leaders are prepared to seize the moment - and if they are able to inspire confidence in each other.

The author is a senior fellow in foreign policy and in the John L. Thornton China Center, The Brookings Institution.